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

Question

asked Dec 28, 2020 103k views

1 Answer

Anand Sunderraman · Answer 1 · 2021-01-02T20:56:50+0000

Answer:

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