Exercise 37 Page 827

Problems involving oblique triangles can be solved by using either the Law of Sines or the Law of Cosines. To decide which of the methods is useful to solve a triangle, we will examine both of these methods one at a time.

Law of Cosines

Let's first draw a triangle.

To solve the above triangle, we can use the Law of Cosines if we know one of the following.

• The measures of two sides and the included angle
• The measures of all three sides

Let's recall the equations of the Law of Cosines. a^2= b^2+ c^2-2 b c * cos A b^2= a^2+ c^2-2 a c * cos B c^2= a^2+ b^2-2 a c * cos C

Law of Sines

Let's again consider a triangle with its measures.

We can use the Law of Sines to solve a triangle if we are given either of the following.

• The measures of two angles and any side
• The measures of two sides and the angle opposite one of the sides

Let's now recall how we form the ratios for the Law of Sines. sin A/a=sin B/b=sin C/c

Conclusion

Here, we can summarize how we decide to choose a method while solving a triangle.