Question

In a 30-60-90 triangle, the length of the side opposite the 30 degree angle is 8. Find the length of the side opposite the 60 degree angle.

Answer 1

Answer:

The length of the side opposite the 60 degree angle 'c' = 4

Step-by-step explanation:

Step(i):-

Given data ∠A = 90° , ∠B = 60° and ∠C = 30°

Given data the length of the side opposite the 30 degree angle is 8

let  'a' = 8

step(ii):-

By using sine rule formula in properties of triangle

$\frac{a}{Sin A} = \frac{b}{Sin B} = \frac{c}{Sin C} = 2 R$

$\frac{a}{Sin A} = \frac{c}{Sin C}$

$\frac{8}{Sin 90} = \frac{c}{Sin 30}$

cross multiplication , we get

$\frac{8 X sin 30}{Sin 90} = c$

we know that trigonometry formulas

sin 30° = $\frac{1}{2}$   and sin 90°= 1

C =  8 X 1/2 = 4

conclusion:-

The length of the side opposite the 60 degree angle 'c' = 4