### Math Notes

Subjects

#### Trigonometry Solutions

##### Topics || Problems

At a point A south of a tower the angle of elevation of the top of the tower is 50 o. At another point B 200 meters east of A, the angle of elevation is 22o. Find the height of the tower.

Height of the tower (CD)

$$\tan 50^o = \frac{CD}{AC}$$

$$AC = \frac{CD}{\tan 50^o}$$

$$\tan 22^o = \frac{CD}{CB}$$

$$CB = \frac{CD}{\tan 22^o}$$

$$(AC)^2 +(AB)^2 = (CB)^2$$

$$(\frac{CD}{ \tan 50^o})^2 +(200)^2 = (\frac{CD}{\tan 22^o})^2$$

$$200^2 = 5.42197 CD^2$$

$$CD = 85.89 m$$