Question

Can you show how to solve? Solve for the unknown(s) in each diagram below. Lines that appear parallel are parallel and each given angle is considered exact.

Answer 1

In the given diagram, angle "p" and the base angle of the right triangle are corresponding angles, which means that they are congruent.

We know both legs of the right triangle, using this information and the trigonometric ratio that relates these sides with the measure of the angle, we can calculate the measure of the angle:

`\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \theta=\tan ^(-1)((opposite)/(adjacent)) \end{gathered}`

Where "θ" represents the base angle of the triangle.

Its adjacent side measures 200m and its opposite side measures 100m, you can calculate the measure of the angle as the inverse tangent of the quotient between the opposite and adjacent sides:

`\begin{gathered} \theta=\tan ^(-1)((100)/(200)) \\ \theta=26.565º \\ \theta\cong26.57º \end{gathered}`

As mentioned before, the angle of elevation, which I named "θ" and the angle of depression, named "p" are congruent so that:

`\theta=p=26.57º`