Use the Law of Sines to solve the triangle? 6.) A=60 degrees, a=9, c=10.

1 Answer
Jan 1, 2017

Check for the Ambiguous Case and, if appropriate, use the Law of Sines to solve the triangle(s).

Explanation:

Here is a reference for The Ambiguous Case

A is acute. Compute value of h:

h=(c)sin(A)

h=(10)sin(60)

h8.66

h<a<c, therefore, two possible triangles exist, one triangle has Cacute and the other triangle has Cobtuse

Use The Law of Sines to compute Cacute

sin(Cacute)c=sin(A)a

sin(Cacute)=sin(A)ca

Cacute=sin1(sin(A)ca)

Cacute=sin1(sin(60)109)

Cacute74.2

Find the measure for angle B by subtracting the other angles from 180:

B=1806074.2

B=45.8

Use the Law of Sines to compute the length of side b:

side b=asin(B)sin(A)

b=9sin(45.8)sin(60)

b7.45

For the first triangle:

a=9,b7.45,c=10,A=60,B45.8,andC74.2

Onward to the second triangle:

Cobtuse180Cacute

Cobtuse18074.2105.8

Find the measure for angle B by subtracting the other angles from 180:

B=18060105.814.2

Use the Law of Sines to compute the length of side b:

b=9sin(14.2)sin(60)

b2.55

For the second triangle:

a=9,b2.55,c=10,A=60,B14.2,andC105.8