Question

Solve triangle ABC if A = 50°, a = 10, and b = 20. If no triangle exists, explain why.

Answer 1

No triangle exists

Explanation:

Angle B=? ------- a/sin(A)= b/sin (B) ------- substitute the given values ------- 10/sin(50º)=20/sin(B) ------- sin(B)=20(sin(50º))/10 ------- sin(B)=1.532

But the max value of sines is 1, so that means that no triangle exists.

Answer 2

No triangle exist

Explanation:

step 1

Find the measure of angle B

Applying the law of sines

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

substitute the given values

`(10)/(sin(50^o))=(20)/(sin(B))`

`sin(B)=20(sin(50^o))/10`

`sin(B)=1.532`

Remember that

The maximum value of the sine is 1

therefore

No triangle exist