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 law of sines: $\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c}$

Explanation:

Step1: Identify trigonometric relation

We have a right - triangle with an angle of elevation of 28° and the opposite side (height of vertical beam) of length 1.6 meters. We want to find the adjacent side $x$. We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.
$\tan(28^{\circ})=\frac{1.6}{x}$

Step2: Solve for $x$

$x = \frac{1.6}{\tan(28^{\circ})}$.
We know that $\tan(28^{\circ})\approx0.5317$, so $x=\frac{1.6}{0.5317}\approx3.0$ meters.

Answer:

3.0 meters