Question

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

Answer 1

m∠B = 100°

a = 4.6

b = 7.36

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