Question

In ABC, if the lengths of sides a and c are 8 centimeters and 16 centimeters, respectively, and the measure of C is 35 degrees, what is the measure of A to two decimal places

Answer 1

∠ A ≈ 16.67°

Explanation:

Using the Sine rule in Δ ABC

`(a)/(sinA)` =
`(c)/(sinC)` , substitute values

`(8)/(sinA)` =
`(16)/(sin35)` ( cross- multiply )

16 sinA = 8 sin35° ( divide both sides by 16 )

sin A =
`(8sin35)/(16)` , thus

∠ A =
`sin^(-1)` (
`(8sin35)/(16)` ) ≈ 16.67° ( to 2 dec. places )