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: Identify the trigonometric relationship

We have a right - triangle where the height of the vertical beam is the opposite side ($y = 1.6$ meters) to the given angle $\theta=28^{\circ}$, and the distance along the horizontal floor ($x$) is the adjacent side to the angle. We use the tangent function, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Set up the equation

$\tan(28^{\circ})=\frac{1.6}{x}$.

Step3: Solve for $x$

$x=\frac{1.6}{\tan(28^{\circ})}$.
We know that $\tan(28^{\circ})\approx0.5317$, so $x=\frac{1.6}{0.5317}\approx 3.0$ meters.

Answer:

3.0 meters