Question

trigonometry help how to set up the triangle

A Prairie dog runs 80 meters down a straight slope from the top to the bottom of a hill. The angle of elevation to the top of the hill from where the Prairie dog is now is 50.425°. When she reaches the bottom of the hill and sees a fox, the prairie dog digs a tunnel nto the hill, parallel with the flat ground, until she is directly under the very top of the hill. How many total meters did the Prairie dog run? Sketch the problem situation

Answer 1

Ok, I'll tell you in words what's going on, then we will look at the triangle. This is a right triangle and the hypotenuse is 80. The angle of elevation is the angle from the ground to the top of the hill inside the triangle. so in order to find the length of the base of the triangle, you need to find the cos(50.425)= x/80 or the side adjacent to the angle over the hypotenuse. This comes out to be 50.96 (make sure your calculator is in degrees and not radians). So if she originally ran the80 meters and then dug back the 50.96 meters, she ran a total of 80 + 50.96.

Answer 2

c my attachment