Question

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that ∠B1 is larger than ∠B2.) a = 31, c = 42, ∠A = 39° ∠B1 = ° ∠B2 = ° ∠C1 = ° ∠C2 = ° b1 = b2 =

Answer 1

Explanation:

In triangle ABC we have
`a = 31, c = 42, ∠A = 39°`

To find other sides and angles.

Use sine formula for triangles

`(a)/(sin A) =(b)/(sin B) =(c)/(sinC) \\(31)/(sin39) =(b)/(sinB) =(42)/(sinc)`

Cross multiply to get

`Angle C =58.5^(o)` or
`121.5`

Angle B = 180-A-C

=
`82.5^(o)` or
`19.5`

b =18.84 or 16.44

There are two triangles

with

`Side a = 31\\Side b = 48.84\\Side c = 42\\Angle ∠A = 39° \\Angle ∠B = 82.50° \\Angle ∠C = 58.5°`

`Side a = 31\\Side b = 16.44204\\Side c = 42\\Angle ∠A = 39° \\Angle ∠B = 19.5° \\Angle ∠C = 121.5°`