Question

a spotlight on the ground shines a beam of light to the top of a tree that is 12 m tall. the beam of light makes an angle of 40° with the ground. what is the distance from the spotlight to the base of the tree, rounded to the nearest meter? 10 m 14 m 16 m 19 m

Explanation:

Step1: Use trigonometric ratio

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 40^{\circ}\), the opposite side (height of the tree) \(y = 12\) m, and the adjacent side (distance from the spotlight to the base of the tree) is \(x\). So, \(\tan40^{\circ}=\frac{12}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x=\frac{12}{\tan40^{\circ}}\). Since \(\tan40^{\circ}\approx0.8391\), then \(x=\frac{12}{0.8391}\approx14.3\).

Answer:

\(14\) m