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? 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 (opposite side to the given angle) is $y = 1.6$ meters and the angle of elevation is $\theta=25^{\circ}$. We want to find the distance $x$ (adjacent side to the angle) on the horizontal floor. We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.
$\tan\theta=\frac{y}{x}$

Step2: Solve for $x$

Given $\theta = 25^{\circ}$ and $y = 1.6$ meters, we can re - arrange the formula $\tan\theta=\frac{y}{x}$ to $x=\frac{y}{\tan\theta}$. Substitute $\theta = 25^{\circ}$ and $y = 1.6$ into the formula. $\tan(25^{\circ})\approx0.4663$, so $x=\frac{1.6}{0.4663}\approx3.43$ meters.

Answer:

3.4 meters