Question

In triangle ABC, m A = 25°, m B = 55°, and a = 10.73. Use the law of sines to find b. Round your answer to the nearest tenth.

Answer 1

20.8 option A

Explanation:

sine law for triangle states that

sin A / a = sin B / b = sin C / c ( equation for sine law )

where m A = 25°

m B = 55°

a = 10.73

b = unknown

from the equation for sine law

sin m A / a = sin m B / b

sin 25° / 10.73 = sin 55° / b

0.4226 / 10.73 = 0.8191 / b

0.0394 = 0.8191 / b equation 2

cross multiply equation 2 becomes

0.0394 b = 0.8191

therefore b = 0.8191 / 0.0394 = 20.789 to the nearest tenth will be 20.8

Answer 2

Option A.
`b=20.8\ units`

Explanation:

we know that

Applying the law of sines

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

substitute the values and solve for b

`(10.73)/(sin(25\°))=(b)/(sin(55\°))\\ \\ b=10.73*sin(55\°)/sin(25\°)\\ \\b=20.8\ units`