Question

question 10 of 12
a 12 - foot board rests against a wall. the angle that the board makes with the ground is 60°. how far is the base of the board away from the wall?
select the correct trig ratio and distance from wall.
a. cos 60° = $\frac{x}{12}$; x = 6 feet
b. sin 60° = $\frac{x}{12}$; x≈10.39 feet
c. sin 60° = $\frac{12}{x}$; x≈13.85 feet
d. cos 60° = $\frac{12}{x}$; x = 24 feet

Explanation:

Step1: Identify triangle sides

Hypotenuse=12ft, adjacent=x, angle=60°.

Step2: Choose trig ratio

cosθ=adjacent/hypotenuse → cos60°=x/12.

Step3: Solve for x

x=12×cos60°=12×0.5=6ft.

Answer:

A. cos 60° = x/12; x = 6 feet