In a right triangle, one of the angles is always 90 degrees (the right angle). Since the sum of the angles in any triangle is always 180 degrees, the third angle can be found by subtracting the measure of the right angle and the given angle from 180.
Thus, the third angle = 180 - 90 - 65 = 25 degrees.
if a right triangle has an angle that is 65 degrees, what is the third angle in the triangle
21 answers
what is the measure of the exterior angle x
the picture shows a right triangle with an angle of 37 and an angle of 42
the picture shows a right triangle with an angle of 37 and an angle of 42
To find the measure of the exterior angle (x), we need to use the property that the sum of the measures of the exterior angles of any polygon is always 360 degrees.
In a triangle, we have three interior angles. The measure of the third angle can be found by subtracting the given angles from 180 degrees:
Third angle = 180 - 37 - 42 = 101 degrees
The exterior angle (x) is formed by extending one of the sides of the triangle. Since the interior and exterior angles are supplementary (they add up to 180 degrees), we can find the measure of the exterior angle as:
x = 180 - 101 = 79 degrees
Therefore, the measure of the exterior angle (x) in the given right triangle is 79 degrees.
In a triangle, we have three interior angles. The measure of the third angle can be found by subtracting the given angles from 180 degrees:
Third angle = 180 - 37 - 42 = 101 degrees
The exterior angle (x) is formed by extending one of the sides of the triangle. Since the interior and exterior angles are supplementary (they add up to 180 degrees), we can find the measure of the exterior angle as:
x = 180 - 101 = 79 degrees
Therefore, the measure of the exterior angle (x) in the given right triangle is 79 degrees.
if a triangle has sides of length 12 and 16, how long is the hypotenuse?
To find the length of the hypotenuse in a right triangle given the lengths of the other two sides, you can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's call the length of the hypotenuse "c," and the lengths of the other two sides "a" and "b."
Applying the Pythagorean theorem, we have:
c^2 = a^2 + b^2
In this case, the lengths of the other two sides are given as 12 and 16:
c^2 = 12^2 + 16^2
c^2 = 144 + 256
c^2 = 400
To find c, we take the square root of both sides:
c = √400
c = 20
Therefore, the length of the hypotenuse is 20 units.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's call the length of the hypotenuse "c," and the lengths of the other two sides "a" and "b."
Applying the Pythagorean theorem, we have:
c^2 = a^2 + b^2
In this case, the lengths of the other two sides are given as 12 and 16:
c^2 = 12^2 + 16^2
c^2 = 144 + 256
c^2 = 400
To find c, we take the square root of both sides:
c = √400
c = 20
Therefore, the length of the hypotenuse is 20 units.
if a right triangle has a leg with length 12 and the hypotenuse is 16, how long is the other leg? round to the nearest tenth if necessary.
To find the length of the other leg in a right triangle given one leg and the hypotenuse, you can use the Pythagorean theorem.
Let's call the length of the known leg "a," the length of the other leg "b," and the length of the hypotenuse "c."
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Applying the Pythagorean theorem, we have:
c^2 = a^2 + b^2
In this case, the length of one leg is given as 12 and the hypotenuse as 16. We'll let the length of the other leg be "b":
16^2 = 12^2 + b^2
256 = 144 + b^2
256 - 144 = b^2
112 = b^2
To find b, we take the square root of both sides:
b = √112
b ≈ 10.6
Therefore, the length of the other leg is approximately 10.6 units (rounded to the nearest tenth).
Let's call the length of the known leg "a," the length of the other leg "b," and the length of the hypotenuse "c."
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Applying the Pythagorean theorem, we have:
c^2 = a^2 + b^2
In this case, the length of one leg is given as 12 and the hypotenuse as 16. We'll let the length of the other leg be "b":
16^2 = 12^2 + b^2
256 = 144 + b^2
256 - 144 = b^2
112 = b^2
To find b, we take the square root of both sides:
b = √112
b ≈ 10.6
Therefore, the length of the other leg is approximately 10.6 units (rounded to the nearest tenth).
a shortstop is standing in the base path between second and third base she finds the ball. She is 30 feet from second base and needs to make the throw to first base. assuming the field is square, how far does she need to throw the ball? round your answer to the nearest tenth
If the shortstop is standing between second and third base and needs to throw the ball to first base, we can visualize a right triangle formed by the positions of the shortstop, second base, and first base.
Let's label the distance between the shortstop and first base as "x," the distance between the shortstop and second base as 30 feet, and the distance between second base and first base as "y."
Using the Pythagorean theorem, we have:
x^2 = 30^2 + y^2
Since the field is assumed to be square, the distance from second base to first base (y) is equal to the distance from second base to third base, which is also 30 feet.
Plugging in the values, we have:
x^2 = 30^2 + 30^2
x^2 = 900 + 900
x^2 = 1800
To find x, we take the square root of both sides:
x = √1800
x ≈ 42.4
Therefore, the shortstop needs to throw the ball approximately 42.4 feet (rounded to the nearest tenth) to reach first base.
Let's label the distance between the shortstop and first base as "x," the distance between the shortstop and second base as 30 feet, and the distance between second base and first base as "y."
Using the Pythagorean theorem, we have:
x^2 = 30^2 + y^2
Since the field is assumed to be square, the distance from second base to first base (y) is equal to the distance from second base to third base, which is also 30 feet.
Plugging in the values, we have:
x^2 = 30^2 + 30^2
x^2 = 900 + 900
x^2 = 1800
To find x, we take the square root of both sides:
x = √1800
x ≈ 42.4
Therefore, the shortstop needs to throw the ball approximately 42.4 feet (rounded to the nearest tenth) to reach first base.
apply the pythagorean theorem to find the length between the two points. The graph shows two points, one at 3, 2, and another at 7, 8. round your answer to the nearest tenth
To find the length between two points using the Pythagorean theorem, we need to consider the distances along the horizontal (x) and vertical (y) axes.
The formula for the distance between the two points (x₁, y₁) and (x₂, y₂) is given by:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
In this case, the first point is (3, 2) and the second point is (7, 8). Applying the formula, we have:
d = √((7 - 3)² + (8 - 2)²)
d = √(4² + 6²)
d = √(16 + 36)
d = √52
d ≈ 7.2
Therefore, the length between the two given points is approximately 7.2 units (rounded to the nearest tenth).
The formula for the distance between the two points (x₁, y₁) and (x₂, y₂) is given by:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
In this case, the first point is (3, 2) and the second point is (7, 8). Applying the formula, we have:
d = √((7 - 3)² + (8 - 2)²)
d = √(4² + 6²)
d = √(16 + 36)
d = √52
d ≈ 7.2
Therefore, the length between the two given points is approximately 7.2 units (rounded to the nearest tenth).
apply the pythagorean theorem to find the length between the two points. The graph shows two points, one at 3, 2, and another at 7, 8. round your answer to the nearest hundredth
To find the length between the two points using the Pythagorean theorem, we need to consider the distances along the horizontal (x) and vertical (y) axes.
The formula for the distance between the two points (x₁, y₁) and (x₂, y₂) is given by:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
In this case, the first point is (3, 2) and the second point is (7, 8). Applying the formula, we have:
d = √((7 - 3)² + (8 - 2)²)
d = √(4² + 6²)
d = √(16 + 36)
d = √52
d ≈ 7.21
Therefore, the length between the two given points is approximately 7.21 units (rounded to the nearest hundredth).
The formula for the distance between the two points (x₁, y₁) and (x₂, y₂) is given by:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
In this case, the first point is (3, 2) and the second point is (7, 8). Applying the formula, we have:
d = √((7 - 3)² + (8 - 2)²)
d = √(4² + 6²)
d = √(16 + 36)
d = √52
d ≈ 7.21
Therefore, the length between the two given points is approximately 7.21 units (rounded to the nearest hundredth).
find the length of the diagonal of the prism. the picture shows a prism with a side the length of 4 cm, a side the length of 3 cm, and a side the length of 12 cm
To find the length of the diagonal of the prism, we can use the Pythagorean theorem. The diagonal represents the hypotenuse of a right triangle formed by two of the sides of the prism.
We have a right triangle with sides of length 4 cm, 3 cm, and the diagonal that we need to find.
Using the Pythagorean theorem, we have:
diagonal^2 = 4^2 + 3^2
diagonal^2 = 16 + 9
diagonal^2 = 25
To find the diagonal, we take the square root of 25:
diagonal = √25
diagonal = 5
Therefore, the length of the diagonal of the prism is 5 cm.
We have a right triangle with sides of length 4 cm, 3 cm, and the diagonal that we need to find.
Using the Pythagorean theorem, we have:
diagonal^2 = 4^2 + 3^2
diagonal^2 = 16 + 9
diagonal^2 = 25
To find the diagonal, we take the square root of 25:
diagonal = √25
diagonal = 5
Therefore, the length of the diagonal of the prism is 5 cm.
the Great pyramid of Giza in Egypt has a square base with edge length of 230.5 m and a slant height of 180.2 m. Find the height of the pyramid. round the answer to the nearest tenth
To find the height of the pyramid, we can use the Pythagorean theorem.
Let's label the height of the pyramid as "h," and we have the following triangle formed by the slant height, height, and half of the base (since the base is a square):
Using the Pythagorean theorem, we have:
h^2 + (230.5/2)^2 = 180.2^2
Simplifying the equation, we have:
h^2 + 26588.5^2 = 32544.04
h^2 = 32544.04 - 26588.5^2
h^2 ≈ 314035.45
To find h, we take the square root of both sides:
h ≈ √314035.45
h ≈ 560.8
Therefore, the height of the Great Pyramid of Giza is approximately 560.8 meters (rounded to the nearest tenth).
Let's label the height of the pyramid as "h," and we have the following triangle formed by the slant height, height, and half of the base (since the base is a square):
Using the Pythagorean theorem, we have:
h^2 + (230.5/2)^2 = 180.2^2
Simplifying the equation, we have:
h^2 + 26588.5^2 = 32544.04
h^2 = 32544.04 - 26588.5^2
h^2 ≈ 314035.45
To find h, we take the square root of both sides:
h ≈ √314035.45
h ≈ 560.8
Therefore, the height of the Great Pyramid of Giza is approximately 560.8 meters (rounded to the nearest tenth).
keysha is building a coffee table. its going to be in the shape of a rectangular prism, without the faces. She wants to make the table decorative by adding metal diagonals. The length of the coffee table will be 44 in., the width 24 in., and the height 14 in. Find the length Keysha should make each diagonal. round the answer to the nearest tenth
To find the length of each diagonal Keysha should make for the coffee table, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the diagonals will act as the hypotenuse of right triangles within the rectangular prism.
Let's consider the three dimensions of the coffee table.
Length = 44 in.
Width = 24 in.
Height = 14 in.
Now let's find the length of each diagonal using the Pythagorean theorem.
Diagonal 1: Connecting the bottom-left corner to the top-right corner
d₁ = √(44^2 + 24^2)
d₁ = √(1936 + 576)
d₁ = √(2512)
d₁ ≈ 50.12
Diagonal 2: Connecting the bottom-left corner to the top-front corner
d₂ = √(44^2 + 14^2)
d₂ = √(1936 + 196)
d₂ = √(2132)
d₂ ≈ 46.17
Diagonal 3: Connecting the bottom-right corner to the top-front corner
d₃ = √(24^2 + 14^2)
d₃ = √(576 + 196)
d₃ = √(772)
d₃ ≈ 27.8
Therefore, the length Keysha should make each diagonal for the coffee table, rounded to the nearest tenth, is approximately:
d₁ ≈ 50.1 in.
d₂ ≈ 46.2 in.
d₃ ≈ 27.8 in.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the diagonals will act as the hypotenuse of right triangles within the rectangular prism.
Let's consider the three dimensions of the coffee table.
Length = 44 in.
Width = 24 in.
Height = 14 in.
Now let's find the length of each diagonal using the Pythagorean theorem.
Diagonal 1: Connecting the bottom-left corner to the top-right corner
d₁ = √(44^2 + 24^2)
d₁ = √(1936 + 576)
d₁ = √(2512)
d₁ ≈ 50.12
Diagonal 2: Connecting the bottom-left corner to the top-front corner
d₂ = √(44^2 + 14^2)
d₂ = √(1936 + 196)
d₂ = √(2132)
d₂ ≈ 46.17
Diagonal 3: Connecting the bottom-right corner to the top-front corner
d₃ = √(24^2 + 14^2)
d₃ = √(576 + 196)
d₃ = √(772)
d₃ ≈ 27.8
Therefore, the length Keysha should make each diagonal for the coffee table, rounded to the nearest tenth, is approximately:
d₁ ≈ 50.1 in.
d₂ ≈ 46.2 in.
d₃ ≈ 27.8 in.
give only one length
The length of the diagonal Keysha should make for the coffee table, rounded to the nearest tenth, is approximately 50.1 inches.
1 answer