law of cosine

Question

In triangle PQR, if r=4, q=5 and cos P= -2/5, find p in simplest radical form

Answer 1

Given PQR triangle.

Sides are r = 4, q = 5

Use law of cosines p^2 = q^2+r^2-2qr CosP

p^2 = (5)^2+(4)^2-2(5)(4) Cos(-2/5)

p^2 = 25+16-40 Cos(-0.4)

p^2 = 1Cos(0.4)

p^2 = 0.99

p = Sqrt(0.99)

 

 

Comments

Solution in simplest radical form .

Answer 2

In PQR triangle P,Q,R are angles and sides are p,q,r.

From law of cosines

Substitute r = 4, q = 5 and P = -2/5 in above formula.

cos(-x) = cosx

Apply squre root on each side.

By using calculator

Solution in simplest radical form .