How many solutions does a triangle with side lengths a = 4, A = 68⁰ and b = 10 have?

Solution:

Given, a triangle has side lengths a = 4 and b = 10

Also, ∠A = 68°

We have to determine how many solutions the given triangle can have.

By using the Law of Sines,

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

So, sin(B) = (b/a)sin(A)

sin(B) = (10/4) sin 68°

= (5/2)(0.9272)

= 2.5(0.9272)

sin(B) = 2.318

We know that the sine of an angle cannot give a value greater than one.

Since sin(B) is greater than one, there are no solutions.

Therefore, no triangle can be built using the given data.

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How many solutions does a triangle with side lengths a = 4, A = 68⁰ and b = 10 have?

Summary:

There are no solutions to a triangle with side lengths a = 4, b = 10 and ∠A = 68°.