a support beam needs to be placed at a 28° angle of elevation so that the top meets a vertical beam 1.6…
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: $\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c}$
Answer
- First, identify the trig - function to use:
- We have a right - triangle where the height of the vertical beam (opposite side with respect to the given angle) is (y = 1.6) meters and the angle of elevation is (\theta=28^{\circ}), and we want to find the distance (x) (adjacent side with respect to the given angle) along the horizontal floor.
- The trigonometric function that relates the opposite side and the adjacent side of a right - triangle is the tangent function. The formula for the tangent of an angle (\theta) in a right - triangle is (\tan\theta=\frac{\text{opposite}}{\text{adjacent}}).
- Then, substitute the known values into the formula:
- Given (\theta = 28^{\circ}) and the opposite side (y = 1.6) meters, and we want to find the adjacent side (x). So, (\tan\theta=\tan(28^{\circ})=\frac{1.6}{x}).
- We know that (\tan(28^{\circ})\approx0.5317). Then, (x=\frac{1.6}{\tan(28^{\circ})}).
- Substituting the value of (\tan(28^{\circ})), we get (x=\frac{1.6}{0.5317}\approx3.0) meters.