Trigonometry Solutions
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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)
\( \tan 50^o = \frac{CD}{AC}\)
\( AC = \frac{CD}{\tan 50^o}\)
\( \tan 22^o = \frac{CD}{CB}\)
\( CB = \frac{CD}{\tan 22^o}\)
\( (AC)^2 +(AB)^2 = (CB)^2 \)
\( (\frac{CD}{ \tan 50^o})^2 +(200)^2 = (\frac{CD}{\tan 22^o})^2 \)
\( 200^2 = 5.42197 CD^2\)
\(CD = 85.89 m\)