Question

question 1 of 26
a 6 foot long board is propped against the wall of a house.
the board forms a 60° angle with the ground. how far is
the base of the board from the wall?

a. 4 ft

b. 4.5 ft

c. 3.5 ft

d. 3 ft

Explanation:

Step1: Identify the triangle type

We have a right triangle (wall, ground, board), with hypotenuse (board) = 6 ft, angle with ground = \(60^\circ\), and we need the adjacent side (distance from base to wall, let's call it \(x\)).

Step2: Use cosine function

In a right triangle, \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 60^\circ\), hypotenuse = 6, adjacent = \(x\). So \(\cos(60^\circ)=\frac{x}{6}\).

Step3: Solve for \(x\)

We know \(\cos(60^\circ)=\frac{1}{2}\), so \(\frac{1}{2}=\frac{x}{6}\). Multiply both sides by 6: \(x = 6\times\frac{1}{2}=3\) ft.

Answer:

D. 3 ft