Question

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle. Then solve the triangle.

a = 8, c = 5,     B = 40^o

Answer 1

Step 1:

The sides of a triangle are and .

The angle of triangle .

To solve the triangle, use Law of Sines and Law of Cosines.

Using law of sines formula .

Here two sides and another angle is given.

Hence, to solve the triangle Law of Sines is not consider.

Step 2:

To solve the triangle by using Law of cosines  formula .

Substitute , and in cosine formula.

Step 3:

To find other two angles, by using law of cosines formula .

The sum of three angles in a triangle

Solution:

, and .