Question
If you have a 24-ft ladder that is landing against the building and touching the ground six feet from the building how high up the building is the top of the ladder
a: 6^2 + b^2 = 24^2; 23.24 ft
b: 24^2 + 6^2 = c^2; 24.7 ft
c: 6^2 + b^2 = 24^2 ; 24.7 ft
d: a^2 + 24^2 = 6^2; 23.24 ft
a: 6^2 + b^2 = 24^2; 23.24 ft
b: 24^2 + 6^2 = c^2; 24.7 ft
c: 6^2 + b^2 = 24^2 ; 24.7 ft
d: a^2 + 24^2 = 6^2; 23.24 ft
Answers
Answer
How far is it from the lighthouse to the ship horizontally if the lighthouse is 20 ft tall and shines a beam to the ship 25 ft long? Also, which statement is correct? (1 point)
a: x = approximately 24.5 yards; from the top of the lighthouse to the boat must be the shortest distance
b: x = 225 feet; the distance from the lighthouse to the ship must be the longest distance
c: x = 15 ft; the distance from the lighthouse to the ship must be the shortest distance
d: x = 15 ft; the distance from the top of the lighthouse to the ship must be the longest distance
a: x = approximately 24.5 yards; from the top of the lighthouse to the boat must be the shortest distance
b: x = 225 feet; the distance from the lighthouse to the ship must be the longest distance
c: x = 15 ft; the distance from the lighthouse to the ship must be the shortest distance
d: x = 15 ft; the distance from the top of the lighthouse to the ship must be the longest distance
Answer
Which of these is a right triangle?
a: triangle 1 has sides of 9, 13, and 14
b: triangle 2 has sides of 5, 6, and 8
c: triangle 3 has sides of 5, 12, and 13
d: triangle 4 has sides of 7, 10, and 12
a: triangle 1 has sides of 9, 13, and 14
b: triangle 2 has sides of 5, 6, and 8
c: triangle 3 has sides of 5, 12, and 13
d: triangle 4 has sides of 7, 10, and 12
Answer
Looking at the right triangle, choose all of the statements that are true. (3 points) Responses Right triangles have side lengths that are always rational numbers. Right triangles have side lengths that are always rational numbers. Right triangles have interior angles that add to equal 180 degrees. Right triangles have interior angles that add to equal 180 degrees. Right triangles have side lengths that always follow a2+b2=c2 Right triangles have side lengths that always follow A squared plus b squared is equal to c squared Right triangles have the pattern that the sum of the two shorter sides = the longest side. Right triangles have the pattern that the sum of the two shorter sides = the longest side. Right triangles must have the side across from the 90 degree angle as the longest side. Right triangles must have the side across from the 90 degree angle as the longest side. Right triangles have interior angles that are all acute angles.
Answer
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Answered by
GPT 3.5
The correct answer is: c) 6^2 + b^2 = 24^2; 24.7 ft
Using the Pythagorean theorem, we can calculate the height up the building where the top of the ladder is located.
Using the Pythagorean theorem, we can calculate the height up the building where the top of the ladder is located.
Answered by
GPT 3.5
In this case, the height of the lighthouse forms one leg of a right triangle, and the beam of light from the top of the lighthouse to the ship forms the hypotenuse of the triangle. The distance from the lighthouse to the ship horizontally forms the other leg of the triangle.
Using the Pythagorean theorem: c^2 = a^2 + b^2, where c is the hypotenuse (25 ft), a is the height of the lighthouse (20 ft), and we want to find b, the distance from the lighthouse to the ship.
25^2 = 20^2 + b^2
625 = 400 + b^2
b^2 = 625 - 400
b = √225 = 15 ft
So, the distance from the lighthouse to the ship is 15 ft.
Therefore, the correct statement is:
c) x = 15 ft; the distance from the lighthouse to the ship must be the shortest distance
Using the Pythagorean theorem: c^2 = a^2 + b^2, where c is the hypotenuse (25 ft), a is the height of the lighthouse (20 ft), and we want to find b, the distance from the lighthouse to the ship.
25^2 = 20^2 + b^2
625 = 400 + b^2
b^2 = 625 - 400
b = √225 = 15 ft
So, the distance from the lighthouse to the ship is 15 ft.
Therefore, the correct statement is:
c) x = 15 ft; the distance from the lighthouse to the ship must be the shortest distance
Answered by
GPT 3.5
In a right triangle, one of the angles must be a 90-degree angle.
We can use the Pythagorean theorem to check if the given triangles are right triangles. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's check for each triangle:
a: 9^2 + 13^2 = 81 + 169 = 250
14^2 = 196
Therefore, triangle 1 with sides 9, 13, and 14 is not a right triangle.
b: 5^2 + 6^2 = 25 + 36 = 61
8^2 = 64
Therefore, triangle 2 with sides 5, 6, and 8 is not a right triangle.
c: 5^2 + 12^2 = 25 + 144 = 169
13^2 = 169
Therefore, triangle 3 with sides 5, 12, and 13 is a right triangle.
d: 7^2 + 10^2 = 49 + 100 = 149
12^2 = 144
Therefore, triangle 4 with sides 7, 10, and 12 is not a right triangle.
So, the right triangle is:
c: triangle 3 has sides of 5, 12, and 13
We can use the Pythagorean theorem to check if the given triangles are right triangles. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's check for each triangle:
a: 9^2 + 13^2 = 81 + 169 = 250
14^2 = 196
Therefore, triangle 1 with sides 9, 13, and 14 is not a right triangle.
b: 5^2 + 6^2 = 25 + 36 = 61
8^2 = 64
Therefore, triangle 2 with sides 5, 6, and 8 is not a right triangle.
c: 5^2 + 12^2 = 25 + 144 = 169
13^2 = 169
Therefore, triangle 3 with sides 5, 12, and 13 is a right triangle.
d: 7^2 + 10^2 = 49 + 100 = 149
12^2 = 144
Therefore, triangle 4 with sides 7, 10, and 12 is not a right triangle.
So, the right triangle is:
c: triangle 3 has sides of 5, 12, and 13
Answered by
GPT 3.5
The statements that are true about right triangles are:
- Right triangles have side lengths that always follow the pattern of a^2 + b^2 = c^2 (Pythagorean theorem).
- Right triangles have the pattern that the sum of the squares of the two shorter sides is equal to the square of the longest side.
- Right triangles must have the side across from the 90-degree angle as the longest side.
So, the correct statements are:
- Right triangles have side lengths that always follow a^2 + b^2 = c^2 (Pythagorean theorem).
- Right triangles have the pattern that the sum of the two shorter sides equals the longest side.
- Right triangles must have the side across from the 90-degree angle as the longest side.
- Right triangles have side lengths that always follow the pattern of a^2 + b^2 = c^2 (Pythagorean theorem).
- Right triangles have the pattern that the sum of the squares of the two shorter sides is equal to the square of the longest side.
- Right triangles must have the side across from the 90-degree angle as the longest side.
So, the correct statements are:
- Right triangles have side lengths that always follow a^2 + b^2 = c^2 (Pythagorean theorem).
- Right triangles have the pattern that the sum of the two shorter sides equals the longest side.
- Right triangles must have the side across from the 90-degree angle as the longest side.
Answered by
GPT 3.5
Yes, I am confident in the correctness of the answers provided. If you have any further questions or need clarification, feel free to ask!
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