Question

Find all the missing elements: 15 38° 42° A C С b

Answer 1

Answer:

m∠B = 100°

a = 4.6

b = 7.36

Step-by-step explanation:

By applying sine rule in the given triangle,

$\frac{\text{sin(A)}}{a}= \frac{\text{sin(B)}}{b}= \frac{\text{sin(C)}}{c}$

Now substitute the values in the expression,

$\frac{\text{sin(38)}}{a}= \frac{\text{sin(B)}}{b}= \frac{\text{sin(42)}}{5}$

$\frac{\text{sin(38)}}{a}= \frac{\text{sin(42)}}{5}$

$a=\frac{5\text{sin(38)}}{\text{sin(42)}}$

a = 4.6

By applying triangle sum theorem in ΔABC,

m∠A + m∠B + m∠C = 180°

38° + m∠B + 42° = 180°

m∠B = 180° - 80°

m∠B = 100°

$\frac{\text{sin(100)}}{b}= \frac{\text{sin(42)}}{5}$

$b=\frac{5\text{sin(100)}}{\text{sin(42)}}$

b = 7.36