In a right triangle, the angles are always 90 degrees, so the given angles of 30, 60, and 90 degrees do not form a right triangle.
To find the lengths of the other leg and the hypotenuse, we need to use the Pythagorean theorem.
Let's call the length of the other leg "x" and the length of the hypotenuse "y".
According to the Pythagorean theorem, we have:
(x)^2 + (6√3)^2 = (y)^2
Simplifying this equation, we get:
x^2 + 108 = y^2
Since one angle of the triangle is 60 degrees, the ratio of the sides is 1:√3:2.
Therefore, we have x/6√3 = 1/√3
Simplifying this equation, we get:
x = 2√3
Now we can substitute this value to find y:
(2√3)^2 + 108 = y^2
12 + 108 = y^2
120 = y^2
Taking the square root of both sides, we get:
y ≈ √120 ≈ 10.95
So, the length of the other leg is 2√3 and the length of the hypotenuse is approximately 10.95.
the angles to a right triangle are 30, 60, and 90 degrees. the given leg length is 6(sqrt3), what are the lengths of the other leg and the hypotenuse?
11 answers
the length of a 45-45-90 triangle's hypotenuse is 40 inches long. what are the lengths of the two legs?
In a 45-45-90 triangle, the two legs are congruent, and the hypotenuse is √2 times the length of each leg.
Given that the hypotenuse is 40 inches long, we can solve for the length of each leg by dividing the hypotenuse length by √2.
Let's call the length of each leg "x".
x = 40 / √2
To simplify this expression, we multiply the numerator and denominator by √2:
x = (40 / √2) * (√2 / √2)
x = (40√2) / 2
x = 20√2
Therefore, the lengths of the two legs are both 20√2 inches long.
Given that the hypotenuse is 40 inches long, we can solve for the length of each leg by dividing the hypotenuse length by √2.
Let's call the length of each leg "x".
x = 40 / √2
To simplify this expression, we multiply the numerator and denominator by √2:
x = (40 / √2) * (√2 / √2)
x = (40√2) / 2
x = 20√2
Therefore, the lengths of the two legs are both 20√2 inches long.
A pilot flying over the Gulf of Mexico sees an island at an angle of depression of 12 degrees. At this time the horizontal distance from the airplane to the island is 4,812 meters. What is the height of the plane to the nearest meter? (1 point) Responses 4455 meters 4455 meters 1023 meters 1023 meters 1215 meters 1215 meters 823 meters
To solve this problem, we can use the tangent function, which relates the angle of depression, the height of the plane, and the horizontal distance.
Let's call the height of the plane "h". We can set up the following equation:
tan(12°) = h / 4812
To solve for h, we can multiply both sides of the equation by 4812:
h = tan(12°) * 4812
Plugging this into a calculator, we find:
h ≈ 1023 meters
Therefore, the height of the plane is approximately 1023 meters.
Let's call the height of the plane "h". We can set up the following equation:
tan(12°) = h / 4812
To solve for h, we can multiply both sides of the equation by 4812:
h = tan(12°) * 4812
Plugging this into a calculator, we find:
h ≈ 1023 meters
Therefore, the height of the plane is approximately 1023 meters.
To find the height of a tree, scientist Sally moves 160 feet away from the base of the tree and then, with a tool 6 feet tall, measures the angle of elevation to the top of the tree to be 62°. To the nearest foot, what is the height of the tree?(1 point) Responses 141 feet 141 feet 307 feet 307 feet 147 feet 147 feet 301 feet
To solve this problem, we can use the tangent function, which relates the angle of elevation, the height of the tree, and the horizontal distance.
Let's call the height of the tree "h". We can set up the following equation:
tan(62°) = h / 160
To solve for h, we can multiply both sides of the equation by 160:
h = tan(62°) * 160
Plugging this into a calculator, we find:
h ≈ 307 feet
Therefore, the height of the tree is approximately 307 feet.
Let's call the height of the tree "h". We can set up the following equation:
tan(62°) = h / 160
To solve for h, we can multiply both sides of the equation by 160:
h = tan(62°) * 160
Plugging this into a calculator, we find:
h ≈ 307 feet
Therefore, the height of the tree is approximately 307 feet.
You are trying to measure the height of your house but only have a surveyor tool that measures angles and you know your sidewalk is exactly 25 feet from the base of your home. From the sidewalk, you find that the measure of the angle of elevation to the top of your house is 58 degrees. How tall is your house to the nearest foot? Please show all work in order to get full credit. (2 points)
To solve this problem, we can use the tangent function, which relates the angle of elevation, the height of the house, and the horizontal distance.
Let's call the height of the house "h". We can set up the following equation:
tan(58°) = h / 25
To solve for h, we can multiply both sides of the equation by 25:
h = tan(58°) * 25
Plugging this into a calculator, we find:
h ≈ 41.47 feet
Therefore, the height of the house is approximately 41.47 feet, which, to the nearest foot, is 41 feet.
Let's call the height of the house "h". We can set up the following equation:
tan(58°) = h / 25
To solve for h, we can multiply both sides of the equation by 25:
h = tan(58°) * 25
Plugging this into a calculator, we find:
h ≈ 41.47 feet
Therefore, the height of the house is approximately 41.47 feet, which, to the nearest foot, is 41 feet.
a right triangle has two leg lengths of 9 units and 15 units. what is the length of the hypotenuse?
To find the length of the hypotenuse in a right triangle, we can use the Pythagorean theorem.
The theorem states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.
Let's call the length of the hypotenuse "c", and the lengths of the legs "a" and "b".
According to the Pythagorean theorem, we have:
a^2 + b^2 = c^2
Substituting the given values of the legs, we have:
(9)^2 + (15)^2 = c^2
81 + 225 = c^2
306 = c^2
Taking the square root of both sides, we get:
c = √306
Therefore, the length of the hypotenuse is √306 units.
The theorem states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.
Let's call the length of the hypotenuse "c", and the lengths of the legs "a" and "b".
According to the Pythagorean theorem, we have:
a^2 + b^2 = c^2
Substituting the given values of the legs, we have:
(9)^2 + (15)^2 = c^2
81 + 225 = c^2
306 = c^2
Taking the square root of both sides, we get:
c = √306
Therefore, the length of the hypotenuse is √306 units.