Question

If sinA = ${\displaystyle \frac{3}{5}}$, find cosA and tanA.

Answer 1

sinA = ${\displaystyle \frac{3}{5}=\frac{\text{Perpendicular}}{\text{Hypotenuse}}}$

By Pythagoras theorem, we have
⇒ (Hypotenuse)² = (Perpendicular)² + (Base)²
⇒ (Base)2 = (Hypotenuse)² - (Perpendicular)²
⇒ (Base) = ${\displaystyle \sqrt{{\left(\text{Hypotenuse}\right)}^2-{\left(\text{Perpendicular}\right)}^2}}$ 
⇒ (Base)
= ${\displaystyle \sqrt{5^2-3^2}}$
= ${\displaystyle \sqrt{25-9}}$
= ${\displaystyle \sqrt{16}}$
= 4

cos A = ${\displaystyle \frac{\text{Base}}{\text{Hypotenuse}}=\frac{4}{5}}$

tan A = ${\displaystyle \frac{\text{Perpendicular}}{\text{Base}}=\frac{3}{4}}$.