# trigonometry

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two points, A and B, are 526 meters apart on a level strecth of road leading to a hill. The angle of elevation of the hilltop from A is 26deg30mins, and the angle of elevation from B is 36deg40mins. How high is the hill?

• trigonometry -

let c = distance from A to top
angle opposite c = 180 -36.67 = 143.33
angle oposite 526 = 180 - 143.33-26.5 = 10.17
law of sines
sin 10.17/526 = sin 143.33/a
so a = 1779
now
sin 26.5 = h/1779
h = 794

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