Question

A beam rests against a wall, forming a 65 degrees with the floor. Use the function y = 9 sec 0 to find the length of the beam to the nearest tenth of a foot.

Answer 1

We know that the angle formed by the beam and the floor is 65 degrees. We also know that the angle between the beam and the wall is complementary to the angle between the beam and the floor (since the beam is resting against the wall). Therefore, the angle between the beam and the wall is:

90 - 65 = 25 degrees

We can use this angle to find the length of the beam. The function y = 9 sec 0 gives us the length of the beam as it relates to the angle 0. We need to use the angle 25 degrees, so we need to convert it to radians first:

25 degrees * (pi/180) = 0.43633 radians

Now we can use the secant function to find the length of the beam:

y = 9 sec 0.43633
y = 14.1 (rounded to the nearest tenth)

Therefore, the length of the beam is approximately 14.1 feet.