If tan A=3 what is sin A

Question

In a right triangle <A is acute 

Answer 1

To solve this, you need to remember which sides of the right triangle each trig function is the ratio of. Tangent is the ratio of opposite/adjacent. Sine is the ratio of opposite/hypotenuse.

 

Since you know tan A = 3 = 3/1, you can draw the simplest triangle that fulfills this, where side a (opposite angle A) is length 3, and side b (adjacent to angle A) is length 1. Use the Pythagorean theorem, and you find that the hypotenuse c is length √(10).

sin A = opp/hyp = a/c = 3/√(10) or 3√(10)/10 if you need to rationalize the denominator