Question

The hypotenuse of a right-angled triangle is 30 cm. and one of the sides is 18 cm. Find the third side and the sine, consine and the tangent of the angle opposite to the third side.

Answer 1

BC is the third side and let angle opposite to be $\theta$.

$B{C}^2$ = $A{C}^2$ - $A{B}^2$ = ${30}^2$ - ${18}^2$

$B{C}^2$ = (30+18) (30-18)

i.e . $B{C}^2$ = 48 × 12

i.e . $B{C}^2$ = 16 × 36

BC = 4 × 6 = 24 cm

∴ sin $\theta$ = $\frac{24}{30}=\frac{4}{5}$

cos $\theta$ = $\frac{18}{30}=\frac{3}{5}$

tan $\theta$ = $\frac{24}{18}=\frac{4}{3}$