Question

the angle of depression from one mountain summit to another 15.9 degrees. If two mountains differ in height by 430 metres, find the horizontal distance between two summits.

Answer 1

Answer: 1,509.52 meters

Step-by-step explanation:

Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.  

Tan α = opposite side / adjacent side  

Where α is the angle of depression from one mountain to another, the opposite side is the difference between heights, and the adjacent side (x) is the horizontal distance between the two summits.

Replacing with the values given:  

Tan 15.9 = 430/x

Solving for x:

x = 430/ (tan 15.9)

x= 1,509.52 meters

Feel free to ask for more if needed or if you did not understand something.