Question

4. Suppose a security light is set into the ground and aims its light at the top of the building. The angle of elevation of the light is 60 degrees. The building is 9 feet tall. a. What is the distance of the light's base from the bottom of the building? Use a trig function to calculate the distance. b. How long is the light beam? light beam. Use a trig function to calculate the length of the

Answer 1

a) The distance of the light's base from the bottom of the building is approximately: 5.2 ft

b) The length of the beam is approximately: 10.4 ft

Explanation:

First, we have to recognize that we may draw a right triangle to picture our problem. Then, in order to find out the distance of the light's base from the bottom of the building, we need to use the tangent trigonometric function:

tan(angle) = opposite side / adjacent side

We know the angle and the opposite side and we want to find the adjacent side:

adjacent side = opposite side / tan(angle) = 9 ft / tan(60°) = 9 ft / = 9 ft / 1.73 = 5.2 ft

In order to find the length of the light beam, we use Pythagoras Theorem:

leg1²+leg2² = hyp²

Since the length of the beam corresponds to the hypotenuse and since we already know the length of the two legs, it is just a matter of substituting the values:

hyp = square_root(leg1²+leg2²) = square_root(9² + 5.2²) ft = square_root(108.4) ft = 10.4 ft