First slide

Applications of trigonometry

Question

The height of the tower vertically at the orthocenter of the triangle (of sides a, b, c) and subtending $∠ A$ at A is

Difficult

A

$a$
B

$b$
C

$c$
D

$\frac{a + b + c}{3}$

Solution

$I f H i s t h e o r t h o c e n t e r a n d h i s t h e h e i g h t o f t h e t o w e r t h e n$
$\tan A = \frac{h}{A H}$ $a n d$ $A H = 2 R \cos A$
$∴ \frac{h}{2 R \cos A} = \tan A \Rightarrow h = 2 R \sin A = a$

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