Question

Find b, given that a = 18.2, B = 62°, and C = 48°. Round answers to the nearest whole number. Do not use a decimal point or extra spaces in the answer or it will be marked incorrect.

Answer 1

The correct answer is B= 19 degrees

Answer 2

Answer:

17

Step-by-step explanation:

We have been given that in triangle ABC, measure of angle B is 62 degrees and measure of angle C is 48 degrees. The length of side opposite to angle a is 18.2. We are asked to find length of side b.

We will use law of sines to solve for side b.

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

$m\angle A+m\angle B+m\angle C=180^{\circ}\\\\m\angle A+62^{\circ}+48^{\circ}=180^{\circ}$

$m\angle A+110^{\circ}=180^{\circ}$

$m\angle A+110^{\circ}-110^{\circ}=180^{\circ}-110^{\circ}$

$m\angle A=70^{\circ}$

Upon substituting our given values, we will get:

$\frac{18.2}{\text{sin}(70^{\circ})}=\frac{b}{\text{sin}(62^{\circ})}$

$\frac{18.2}{\text{sin}(70^{\circ})}*\text{sin}(62^{\circ})=\frac{b}{\text{sin}(62^{\circ})}*\text{sin}(62^{\circ})$

$\frac{18.2}{\text{sin}(70^{\circ})}*\text{sin}(62^{\circ})=b$

$b=\frac{18.2}{\text{sin}(70^{\circ})}*\text{sin}(62^{\circ})$

$b=\frac{18.2}{0.939692620786}*0.882947592859$

$b=19.1551999*0.882947592859$

$b=16.9130376$

$b\approx 17$

Therefore, the length of side b is 17 units.