Question

In ABC, mA = 46, mB = 105, and c = 19.8. Find a to the nearest tenth.

Answer 1

a = 29.3785

Explanation:

Given ∠A = 46° and ∠B = 105°

we know that ∠A +∠B+∠C = 180°

46° + 105° +∠C = 180°

∠C = 180 - 46 -105

∠ C = 29°

By using sine rule

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

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

Given ∠A = 46° and ∠ C = 29° and c = 19.8

`(a)/(sin 46) = (19.8)/(Sin 29)`

on cross multiplication , we get

`a = (19.8 X sin 46)/(Sin 29)`

a = 29.3785