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

Answer 1

To find the length of the beam, we first need to determine the angle θ that the beam makes with the floor. Since the beam forms a 65° angle with the wall, the angle θ will be the complement of this angle with respect to 90°. So, θ = 90° - 65° = 25°.

Next, we can use the trigonometric function secant to find the length of the beam. The formula for the secant function is:

sec(θ) = hypotenuse / adjacent

In this case, the hypotenuse is the length of the beam, which we want to find, and the adjacent side is the height of the beam (y).

We can rearrange the formula to solve for the length of the beam:

9 = hypotenuse / y

hypotenuse = 9y

Now, we can substitute the angle θ into the equation:

hypotenuse = 9 * sec(25°)

hypotenuse ≈ 23.7 feet

Therefore, the length of the beam is approximately 23.7 feet when rounded to the nearest tenth.