Question

Find all the missing elements

Answer 1

Answer:

$b = 5.5$

$c = 11.2$

Step-by-step explanation:

Given:

A = 96°

B = 25°

C = 59°

a = 13

Required:

b and c

SOLUTION:

Use Sine Rule to find the measure of a and b, respectively.

✍️Thus, to find b, use,

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

Plug in the values

$\frac{13}{sin(96)} = \frac{b}{sin(25)}$

Multiply both sides by sin(25)

$\frac{13}{sin(96)} \times sin(25) = \frac{b}{sin(25)} \times sin(25)$

$\frac{13 \times sin(25)}{sin(96)} = b$

$b = 5.5$ (nearest tenth)

✍️To find c, use,

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

Plug in the values

$\frac{13}{sin(96)} = \frac{c}{sin(59)}$

Multiply both sides by sin(59)

$\frac{13}{sin(96)} \times sin(59) = \frac{c}{sin(25)} \times sin(59)$

$\frac{13 \times sin(59)}{sin(96)} = c$

$c = 11.2$ (nearest tenth)