Question

question 20 of 25
a 15 - 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° = 15/x; x = 30 feet
b. sin 60° = 15/x; x≈17.32 feet
c. cos 60° = x/15; x = 7.5 feet
d. sin 60° = x/15; x≈12.99 feet

Explanation:

Step1: Identify right - triangle and variables

The board forms a right - triangle with the wall and the ground. The length of the board is the hypotenuse $c = 15$ feet, the angle between the board and the ground is $\theta=60^{\circ}$, and we want to find the distance $x$ from the base of the board to the wall (adjacent side to the given angle).

Step2: Select the correct trigonometric ratio

The cosine of an angle in a right - triangle is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\cos60^{\circ}=\frac{x}{15}$.

Step3: Solve for $x$

Since $\cos60^{\circ}=\frac{1}{2}$, we have $\frac{1}{2}=\frac{x}{15}$. Cross - multiplying gives $x = 15\times\cos60^{\circ}=15\times\frac{1}{2}=7.5$ feet.

Answer:

C. $\cos 60^{\circ}=\frac{x}{15};x = 7.5$ feet