Question

How many solutions does a triangle with side lengths a = 6, a equals 110 degree , and b = 10 have?

Answer 1

The Answer is 0. No solution

Answer 2

No solution

Explanation:

We are given some dimension of triangle.

a=6

∠A=110°

b=10

Using sine law, we will find rest part of the triangle.

`(a)/(\sin A)=(b)/(\sin B)=(c)/(\sin C)`

Substitute the value into formula

`(6)/(\sin 110^\circ)=(10)/(\sin B)=(c)/(\sin C)`

`(6)/(\sin 110^\circ)=(10)/(\sin B)`

`\sin B=1.56`

`\angle B=\sin^(-1)(1.56)`

`\angle B=\text{Not Possible}`

Because value of sine can't be more than 1.

No solution for triangle. No such triangle form.

Hence, The number of triangle for given info is zero