Question

From a point P on level ground, the angle of elevation of the top of a tower is 27°10'. From a point 23.0 meters closer to the tower and on the same line with P and the base of the tower, the angle of elevation of the top is 51°30'. Approximate the height of the tower. (to the nearest tenth)

Answer 1

From the Figure above:\[x=h \cot (a)-23 \]and\[x=h \cot (b) \]Equate the RHS of each equation to each other.\[h \cot (a)-23\text{ = }h \cot (b)\]and solve for h.\[h=\frac{23}{\cot (a)-\cot (b)} \]\[a\text{ = }\pi \left.\left(27+\frac{10}{60}\right)\right/180\text{ = }\frac{163 \pi }{1080} \]\[b\text{ = }\pi \left.\left(51+\frac{30}{60}\right)\right/180\text{ = }\frac{103 \pi }{360}\]\[h\text{ = }\frac{23}{\text{Cot }\left[\frac{163 \pi }{1080}\right]-\text{Cot }\left[\frac{103 \pi }{360}\right]}=19.9 \text{ meters}\]

Answer 2

Thanks!