10-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.
Question
10-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.
Solution
To solve this problem, we can use trigonometry. Specifically, we'll use the cosine function, which is defined as adjacent/hypotenuse.
Here, the 10-foot board is the hypotenuse, the wall is the adjacent side, and we're trying to find the distance from the base of the board to the wall, which is the adjacent side.
The cosine of 60° is 0.5. So, we can set up the equation:
cos(60°) = adjacent / hypotenuse 0.5 = adjacent / 10 feet
Solving for the adjacent side, we get:
Adjacent = 0.5 * 10 feet = 5 feet
So, the base of the board is 5 feet away from the wall.
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