Question

Find all the missing elements

Answer 1

`b = 5.5`

`c = 11.2`

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,

`(a)/(sin(A)) = (b)/(sin(B))`

Plug in the values

`(13)/(sin(96)) = (b)/(sin(25))`

Multiply both sides by sin(25)

`(13)/(sin(96)) * sin(25) = (b)/(sin(25)) * sin(25)`

`(13 * sin(25))/(sin(96)) = b`

`b = 5.5` (nearest tenth)

✍️To find c, use,

`(a)/(sin(A)) = (c)/(sin(C))`

Plug in the values

`(13)/(sin(96)) = (c)/(sin(59))`

Multiply both sides by sin(59)

`(13)/(sin(96)) * sin(59) = (c)/(sin(25)) * sin(59)`

`(13 * sin(59))/(sin(96)) = c`

`c = 11.2` (nearest tenth)