Question

If a scalene triangle has its measures 4 m, 11 m and 8 m, find the largest angle.

A. 129.8
B. 90.0
C. 34.0
D. 16.2​

Answer 1

129.8 approximately

Explanation:

So this sounds like a problem for the Law of Cosines. The largest angle is always opposite the largest side in a triangle.

So 11 is the largest side so the angle opposite to it is what we are trying to find. Let's call that angle, X.

My math is case sensitive.

X is the angle opposite to the side x.

Law of cosines formula is:

`x^2=a^2+b^2-2ab \cos(X)`

So we are looking for X.

We know x=11, a=4, and b=8 (it didn't matter if you called b=4 and a=8).

`11^2=4^2+8^2-2(4)(8)\cos(X)`

`121=16+64-64\cos(X)`

`121=80-64\cos(X)`

Subtract 80 on both sides:

`121-80=-64\cos(X)`

`41=-64\cos(X)`

Divide both sides by -64:

`(41)/(-64)=\cos(X)`

Now do the inverse of cosine of both sides or just arccos( )

[these are same thing]

`\arccos((-41)/(64))=X`

Time for the calculator:

X=129.8 approximately