Question

In triangle ABC, b = 600, ∠B = 11°, and ∠C = 75°. Find a.

Answer 1

Knowing 2 of the angles, you can find angle A.
180-11-75=94.
You now know angle A is 94°
You can now use the law of sines to solve.
600/sin11°=a/sin94°
Side a is 3136.85

Answer 2

`a=3,136.85\ units`

Explanation:

Step 1

Find the measure of angle A

we know that

The measure of the internal angles of a triangle is equal to
`180\°`

so

m∠A=
`180\°-11\°-75\°`

m∠A=
`94\°`

Step 2

Find the measure of side a

Applying the law of sines

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

we have

`b=600\ units, B=11\°, A=94\°`

substitute

`(600)/(sin(11\°))=(a)/(sin(94\°))`

`a=600*sin(94\°)/sin(11\°)`

`a=3,136.85\ units`