Question 999146: a hiker approximates an angle at the top of a hill to be 22 degrees. After walking 700 feet closer, the hiker estimates to angle of elevation increased by 16 degrees. How high is the hill?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The height of the hill is x feet above the hiker.
The tangent of the height is x/the distance the hiker is from the perpendicular.
tan 22=0.4040=x/distance(d)
700 feet closer, the angle is now 38 degrees.
The height hasn't changed, but the distance is less
tan 38=0.7813=x/(d-700)
0.7813*(d-700)=0.4040d , because both of these tangents are equal to the same x or height, so they are equal to each other.
0.7813d-546.90=0.404d
0.3773d=546.90
d=1449.51 ft. THAT IS NOT THE HEIGHT, ONLY THE LENGTH OF THE ADJACENT SIDE.
TAN 22=X/1449.51
1449.51*0.404=585.60 FEET
check with the other
749.51*0.7813=585.58 FEET, the same given rounding error.
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