If tan A=10 , find sin A

Question

If tan A=10, find sun A

Answer 1

This problem requires knowing the trig functions of sine and tangent and the Pythagorean Theorem.

Sine = opposite/hypotenuse Tangent = opposite/adjacent)

 

Since tan A = 10 = 20/2, side a (opposite angle A) is length 20 and side b (adjacent to angle A) is length 2. Using the Pythagorean Theorem, you find that the hypotenuse c is length √(404).

sin A = opp/hyp = a/c = 20/√(404)= 20√(404)/404 = 5√(404)/101.