The angle of elevation of the tower from A is 25°. From another point B, the angle of elevation of the top of the tower is 56°. AB=300m and on the same horizontal plane as the foot of the tower. The horizontal angle subtended by A and B at the foot of the tower is 70°.

What is the height of the tower?

How far A from the tower?

How far B from the tower?

$x = h / \tan 25^\circ$

$y = h / \tan 56^\circ$

$300^2 = x^2 + y^2 - 2xy \cos 70^\circ$

$300^2 = \left( \dfrac{h}{\tan 25^\circ} \right)^2 + \left( \dfrac{h}{\tan 56^\circ} \right)^2 - 2\left( \dfrac{h}{\tan 25^\circ} \right)\left( \dfrac{h}{\tan 56^\circ} \right) \cos 70^\circ$

$h = 148.8 ~ \text{m}$

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