You can use the law of sines along with the angle of elevation given to find out the length of the distance of the vertical beam from the lower end of the support beam(horizontally).
The distance between lower end of the support beam from the vertical beam along the horizontal floor is given by
Option A: 3.0 meters
What is law of sines?
For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,
we have, by law of sines,
[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]
Remember that we took
[tex]\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}[/tex]
Using the law of sines, as referring in the figure attached below, we get:
[tex]\dfrac{\sin\angle C}{|AB|} = \dfrac{\sin\angle A}{|BC|}[/tex]
Since in a triangle, the sum of its angle is 180 degrees, thus,
[tex]\angle A + \angle B + \angle C = 180 ^\circ\\\angle A = 180 - 28 - 90 = 62^\circ[/tex]
Using the fact that |AB| = 1.6 meters and that angle C is of 28°, we get
[tex]\dfrac{\sin\angle C}{|AB|} = \dfrac{\sin\angle A}{|BC|}\\\\\dfrac{\sin28^\circ}{1.6} = \dfrac{\sin62^\circ}{|BC|}\\\\\text{Using sin calculator}\\\\\dfrac{0.469}{1.6} = \dfrac{0.8829}{|BC|}\\\\|BC| = \dfrac{0.8829 \times 1.6}{0.469} \approx 3.012 \approx 3 \: \rm meters[/tex]
Thus,
as length of BC = |BC| = 3 meters denote the horizontal length from the vertical beam and the lower end of the support beam, thus,
The distance between lower end of the support beam from the vertical beam along the horizontal floor is given by
Option A: 3.0 meters
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