Question

The resultant of a 15-pound force and an 8-pound force acting on an object is 10 pounds.The angle formed, to the nearest degree, between the resultant and the smaller force is

Answer 1

The angle formed, to the nearest degree, between the resultant and the smaller force is 112°

Explanation:

By using the cosine rule ; a2= b2 + c2 - 2bc cosa

15^2= 8^2 +10^2 - 2×8×10 cos A

225 =64 + 100 - 2×8×10 cosa

225= 164-160cosA

160 cosA= 164-225

CosA= -61/160

A= cos inverse(-0.38125)

A= 112°

Answer 2

`68`

Explanation:

First let use cosine rule to determine the angle opposite to the resultant force of 10lb

`c^(2)=a^(2)+b^(2)-2abcosC\\ 10^(2)=15^(2)+8^(2)-2*15*8cosC\\ C=cos^(-1)(0.7875)\\C=38.04^(0)`

from the diagram in the attachment(not drawn to scale) we can model what the the diagram will look like.

using the sine rule to determine the angle the 10lb make with the 8lb

`(15)/(sin\alpha ) =(10)/(sin38.04) \\sin\alpha =0.9243\\\alpha =sin^(-1)(0.9243)\\ \alpha =67.56`

Hence the angle formed to the nearest degree is
`68`