Krishna
0

Step 1: Recall the cosines formula

The law of cosines is a formula that relates the three sides of a triangle to

the cosine of a given angle

FORMULA: a^2 = b^2 + c^2 - 2bc \cos(A)

b^2 = a^2 + c^2 - 2ac \cos(B)

c^2 = b^2 + a^2 - 2ba \cos(C)

Where each lowercase letter (like a) is the length of the side opposite the

vertex labeled with the same capital letter.

Step 2: Use the cosine formula to find unknown length.

Since you know

The lengths of two sides p = 6.5

q = 7.4

The measure of the included angle \angle PRQ = 58\degree

Unknown length r = ?

Cosines formula

r^2 = p^2 + q^2 - 2pq \cos 58\degree

r^2 = 6.5^2 + 7.4^2 - 2(6.5*7.4) \cos 58\degree

r^2 = 42.25 + 54.76 - 96.20 *0.5299

(\because use\ calculator\ to\ find\ the\cos58\degree\ value)

r^2 = 97.01 - 50.9763

r^2 = 46.03

r = 6.7845