Question

what is the angle formed by the hillside and theo's line of sight p?1 Approximately 104.8 degree2 Approximately 20 degree3 Approximately 55.2 degree 4 Approximately 180 degree

Answer 1

We have to find the angle formed by the hillside and Teo's line of sight (P).

We know two side lenghts and one angle measure.

We can use the Law of sines to relate angles and sides: the quotient between the sine of an angle and its opposite side length is constant for the three pair of angles and opposite sides of the triangle.

In this case we can write:

`\begin{gathered} (\sin20\degree)/(100)=(\sin P)/(80) \\ \sin P=(80)/(100)\sin20\degree \\ \sin P\approx0.8\cdot0.342 \\ \sin P\approx0.274 \\ P\approx\arcsin(0.274) \\ P\approx15.9\degree \end{gathered}`

As the two sides are approximately the same length (80 yd vs 100 yd), we can expect for the opposite angle to have similar measures.

Then, as one of the opposite angles is 20°, the other opposite angle (P) will have a measure that is approximately 20° too.

Answer: 2. Approximately 20 degrees