Question

Select the correct answer. In ΔABC, if the lengths of sides a and c are 8 centimeters and 16 centimeters, respectively, and the measure of ∠C is 35°, what is the measure of ∠A to two decimal places? A. 16.67° B. 17.50° C. 26.57° D. 35.53°

Answer 1

A

Explanation:

using the Sine rule in ΔABC

`(a)/(sinA)` =
`(c)/(sinC)`

substitute given values

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

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

sinA =
`(8sin35)/(16)` = 0.28678...

⇒ A =
`sin^(-1)`(0.28678..) = 16.67° ( to 2 dec. places )