Height of a tower

From a point P on level ground, the angle of elevation of the top of a tower is 26 °50.' From a point 25meters 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 53°30.' Approximate the height of the tower.

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25m

tan 26°50'=height (OPPOSITE)

25m+x

tan53° 30'=h

x

Generalize to the case where the first angle is alpha, the second angle is beta, and the distance between the two points is d. Express the height h of the tower in terms of d, alpha and beta.

ά=tan inversehtx

25 meters

β=90-°ά