The depression angle from the top of this peak to the small miner's cabin is 2000ft and 26 degrees. The cabin is 14,000ft from a point under the peak. Find the altitude of the top of the mountain.

⚑ Flag

Jessica -Thanks for the extra info on the 2000 feet ... the problem is saying that the cabin is 2000 feet above sea level and it is level horizontally with the base of the mountain. So, when we find the distance from the base of the mountain to the peak, we just need to add 2000 to our answer.It is always best to draw a picture:The angle of depression = 26 degreesThe horizontal base = 14000 feetWhat we need to find is the height of the triangle, which is the vertical leg.Here is the trick - the angle between the hypotenuse and the vertical leg = 90 - 26 = 64 degrees, do you agree?Now just use your right triangle formula for Tangent:where x = the height of the vertical leg.Solve for x:I get x = 6,828 feet, but now add 2000 feet to this answer because the cabin is already 2000 feet above sea level.The final answer is 6828 + 2000 = 8828 or 8,800 feet above sea level rounded to the nearest 100 feet.Hope that helps