Question

Some the triangle using the Law of Sines.(round answer to 2 decimal places)

Answer 1

a = 4.64

c = 6.57

B = 75

Explanation:

Law of sines in a triangle:

a, b and c are the sides.

A, B and C are the angles.

They are related in the following way:

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

Applying the law to the triangle in this question:

`(a)/(\sin40)^{^{}}=(7)/(\sin B)=(c)/(\sin65)`

The internal angles of a triangle add up to 180º

65 + B + 40 = 180

105 + B = 180

B = 75

So

`(a)/(\sin40)^{^{}}=(7)/(\sin 75)=(c)/(\sin65)`

The sines are:

sin 40º = 0.64

sin 75º = 0.966

sin 65º = 0.906

Finding a:

`(a)/(\sin 40)=(7)/(\sin 75)`
`(a)/(0.64)=(7)/(0.966)`

Applying cross multiplication:

0.966a = 7*0.64

a = (7*0.64)/0.966

a = 4.64

Finding c:

`(7)/(\sin 75)=(c)/(\sin 65)`
`(7)/(0.966)=(c)/(0.906)`

0.966c = 7*0.906

c = 7*0.906/0.966

c = 6.565