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olga_2 [115]
3 years ago
15

Find all the missing elements

Mathematics
1 answer:
Roman55 [17]3 years ago
3 0

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)

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