1. ## trigonometry

A vertical tower stands on horizontal ground . The angle of elevation on the top T , of the tower from a point P south of the tower is 50 degree and the angle of elevation of T from a point Q west of the tower is 32 degree . Given that the distance PQ is 150 m , calculate the height of the tower .

When the question says south , does it mean exactly south of the tower ? If so , how can it be 50 degree , should be 90 degrees ??

2. Originally Posted by thereddevils
A vertical tower stands on horizontal ground . The angle of elevation on the top T , of the tower from a point P south of the tower is 50 degree and the angle of elevation of T from a point Q west of the tower is 32 degree . Given that the distance PQ is 150 m , calculate the height of the tower .

When the question says south , does it mean exactly south of the tower ? Yes If so , how can it be 50 degree , should be 90 degrees ??
1. Draw a sketch (see attachment)

2. The foot of the tower, P and Q are the vertices of a right triangle because the directions West and South include 90°.

3. Let x, y denote the legs of this right triangle and h the height of the tower. Then you'll get:

$x = \dfrac h{\tan(32^\circ)}$

$y = \dfrac h{\tan(50^\circ)}$

4. Now use Pythagorean theorem:

$x^2 + y^2 = 150^2$ Substitute x and y and solve this equation for h.

3. REally thank you earboth , appreciate that .. Btw what software did u use to draw such diagrams , looks so useful . I bet many hv asked this ..

4. Originally Posted by thereddevils
REally thank you earboth , appreciate that .. Btw what software did u use to draw such diagrams , looks so useful . I bet many hv asked this ..