Question

a support beam needs to be placed at a 28° angle of elevation so that the top meets a vertical beam 1.6 meters above the horizontal floor. the vertical beam meets the floor at a 90° angle.
approximately how far from the vertical beam should the lower end of the support beam be placed along the horizontal floor?
3.0 meters
3.4 meters
3.9 meters
4.4 meters
law of sines: $\frac{\sin(a)}{a} = \frac{\sin(b)}{b} = \frac{\sin(c)}{c}$

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 28^{\circ}\), the opposite side \(y = 1.6\) meters, and the adjacent side is \(x\) (the distance we want to find). So, \(\tan(28^{\circ})=\frac{1.6}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x=\frac{1.6}{\tan(28^{\circ})}\).
We know that \(\tan(28^{\circ})\approx0.5317\). Then \(x=\frac{1.6}{0.5317}\approx3.0\)

Answer:

3.0 meters