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 trigonometric ratio

We have a right triangle, with opposite side to $28^\circ$ equal to 1.6 m, and adjacent side $x$. Use tangent:
$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Step2: Substitute known values

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

Step3: Rearrange to solve for $x$

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

Step4: Calculate the value

$\tan(28^\circ) \approx 0.5317$, so:
$x \approx \frac{1.6}{0.5317} \approx 3.0$

Answer:

3.0 meters