Some Applications Of Trigonometry

Question

Given 15 cot A = 8, find sin A and sec A.

Solution

Let us draw a right triangle ABC, right angled at B.
It is given that:
15 cot A = 8

rightwards double arrow

space space cotA space equals space 8 over 15 equals AB over BC

Let
AB = 8K, BC = 15K
Using Pythagoras theorem, we have
AC² = AB² + BC²= (8K)² + (15K)²= 64K² + 225K²= 289K²So,
AC = 17K
Now,
AC = 17K
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