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

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

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

`(a)/(Sin A) = (b)/(Sin B) = (c)/(Sin C) = 2 R`

`(a)/(Sin A) = (c)/(Sin C)`

`(8)/(Sin 90) = (c)/(Sin 30)`

cross multiplication , we get

`(8 X sin 30)/(Sin 90) = c`

we know that trigonometry formulas

sin 30° =
`(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