Question
find x. There is a right triangle. the height is 48. The top angle is 37 degrees. The hypotenuse is x. find x
Answers
GPT 3.5
To find the length of the hypotenuse (x), we can use the trigonometric function cosine, which relates the adjacent side (height) to the hypotenuse:
cos(angle) = adjacent/hypotenuse
In this case, the adjacent side is the height (48) and the angle is 37 degrees:
cos(37°) = 48/x
Solve for x by multiplying both sides by x:
x * cos(37°) = 48
Divide both sides by cos(37°):
x = 48 / cos(37°)
Using a calculator, we can find the value of cos(37°) ≈ 0.7986.
x ≈ 48 / 0.7986 ≈ 60.11
Therefore, the length of the hypotenuse (x) is approximately 60.11.
cos(angle) = adjacent/hypotenuse
In this case, the adjacent side is the height (48) and the angle is 37 degrees:
cos(37°) = 48/x
Solve for x by multiplying both sides by x:
x * cos(37°) = 48
Divide both sides by cos(37°):
x = 48 / cos(37°)
Using a calculator, we can find the value of cos(37°) ≈ 0.7986.
x ≈ 48 / 0.7986 ≈ 60.11
Therefore, the length of the hypotenuse (x) is approximately 60.11.