How do you solve the description?

Question

A person with height h = 1.7 m is standing on the very top of a hill, pictured below (not to scale). At a distance

d = 4.6 m down the side of the hill, the angle at B (between the hillside and the line going to the top of the person) is 8◦. Find the angle at A to the nearest tenth of a degree.

Continuation. Now use the given information to find the angle (to the nearest tenth of a degree) that the hill makes with the horizontal (ie the angle at C). (Hint: It may help to determine the angle the person makes with the hilltop, and then to draw a horizontal line at the person’s feet to determine the angle the hill makes with the horizontal).

Answer 1

guy is 1.7 meters tall

he's at the top of a hill side

4.6 meters down the hill side makes an angle of 8 degrees

assume the hill has a straight line hillside

draw a straight line from point B, 4.6 meters down the hillside to top of the guy's head and another straight line from point B to his feet. Those two lines form an 8 degree angle

what's the angle A formed by the line of the hillside with the flat earth below?

use the law of sines to solve the top triangle, SSA

then construct some right triangles, top one including the 4.6 as the hypotenuse, with three known angles use the sines law again to find the other 2 sides

continue to solve the other constructed right triangles which include the base at the bottom, which is the distance from B to the point directly below the top of the hill

and the hypotenuse = the full length of the side of the hillside