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

Answer:

A

Step-by-step explanation:

using the Sine rule in ΔABC

$\frac{a}{sinA}$ = $\frac{c}{sinC}$

substitute given values

$\frac{8}{sinA}$ = $\frac{16}{sin35}$ ( cross- multiply )

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

sinA = $\frac{8sin35}{16}$ = 0.28678...

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