Question

What is the measure of Q to the nearest whole degree?

Answer 1

Answer:
`53^(\circ)`

Explanation:

In the given figure , we have a triangle having sides , 18 , 17 and 20.

Law of cosines :-

`a^2=b^2+c^2-2bc\cos(A)`, where a, b and c are the sides of the triangle and A is the angle opposite to side a.

Since angle Q is opposite to side MN with measure 17 .

Put a= 17 , b=18 and c=20 in the equation , we get

`17^2=18^2+20^2-2(18)(20)\cos(Q)\\\\\Rightarrow\ 720\cos(Q)=18^2+20^2-17^2\\\\\Rightarrow\ 720\cos(Q)=435\\\\\Rightarrow\ \cos(Q)=(435)/(720)\\\\\Rightarrow\ \angle{Q}=\cos^(-1)((435)/(720))=0.92207665\text{radian}\\\\\Rightarrow\angle{Q}=0.92207665*(180)/(\pi)\approx53^(\circ)`