To find the length of the beam, we need to set up a right triangle with the beam as the hypotenuse. The angle between the beam and the floor is 65°, so the angle between the beam and the wall is 90° - 65° = 25°.
Let the length of the beam be x. Then, using trigonometry, we have:
sec(25°) = hypotenuse/adjacent
sec(25°) = x/y
y = x/cos(25°)
We are given that y = 9. Therefore:
9 = x/cos(25°)
x = 9cos(25°)
Using a calculator to find cos(25°) ≈ 0.9063 and multiplying by 9, we get:
x ≈ 9(0.9063) ≈ 8.2 ft
Therefore, the length of the beam is approximately 8.2 ft to the nearest tenth of a foot. The answer is 8.2 ft.
A beam rests against a wall, forming a 65° with the floor. Use the function y = 9 sec e to find the length of the beam to
the nearest tenth of a foot.
(1 point)
8.2 ft
21.3 ft
9.9 ft
18.7 ft
1 answer
2 answers