Question

D. 47.2 Math question no Guessing and Please show work

Answer 1

Given that measure of angle A = 72 degree

Given that measure of angle B = 16 degree

We know that sum of all angles of the triangle is 180 degree

A+B+C=180

72+16+C=180

88+C=180

C=180-88

C=92

Hence measure of angle C = 92 degree

Now we can use sine formula to find the missing side "a"

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

$\frac{a}{\sin\left(A\right)}=\frac{c}{\sin\left(C\right)}$

$\frac{a}{\sin\left(72\right)}=\frac{61}{\sin\left(92\right)}$

$\frac{a}{0.951}=\frac{61}{0.99939}$

$\frac{a}{0.951}=61.037232712$

a=61.037232712*0.951

a=58.0464083091

Hence final answer is approx a=58.05