Question

In the figure below, a pole hast two wires attached to it, one on each side, forming two right triangles.
-How tall is the pole?
-How far from the base of the pole does Wire 2 attach to the ground?
-How long is Wire 1?

Answer 1

The side adjacent to the 41° angle is 38ft. The pole is on the opposite side to the 41° angle, so you can use
\[\tan\theta = \frac{\text{opposite}}{\text{adjacent}}\]
\[\tan41^\circ = \frac{\text{height}}{38\text{ ft}}\]

The distance from where wire 2 meets the ground to the base of the pole is the opposite side to the 38° angle, and the pole is the adjacent side
\[\tan38^\circ = \frac{\text{distance from base}}{\text{height}}\]

The length of wire 1 can be worked out 3 ways:
using
\[\sin\theta = \frac{\text{hypotenuse}}{\text{opposite}}\]
\[\sin41^\circ = \frac{\text{length}}{\text{height}}\]
using
\[\cos\theta = \frac{\text{hypotenuse}}{\text{adjacent}}\]
\[\cos41^\circ = \frac{\text{length}}{38\text{ ft}}\]
or using
\[\text{hypotenuse} = \sqrt{(38\text{ ft})^2 + (\text{height})^2}\]

Answer 2

Thanks I knew I had to use tan I just needed better explanation on how to use it. I did this problem in class but the teacher is not so good ate explaining. THANKS!