Question

Find y. Please help!

Answer 1

Answer:

$y\approx 11.9$

Step-by-step explanation:

Here, we have the known angle sandwiched between two known sides.

So, we have SAS.

And we want to find the side opposite to the angle.

Therefore, we can use the Law of Cosines:

$c^2=a^2+b^2-2ab\cos(C)$

Again, it is important what we substitute.

a and b are the two side lengths. So, we will substitute 8 for a and 13 for b.

C is our angle. So, substitute 64 for C.

And c is what we’re trying to solve.

Therefore:

$c^2=(8)^2+(13)^2-2(8)(13)\cos(64)$

Simplify:

$c^2=64+169-208\cos(64)$

Add:

$c^2=233-208\cos(64)$

Take the square root of both sides:

$c=\sqrt{233-\cos(64})$

Use a calculator. So, c is approximately:

$c\approx11.9$

The c is our y. So, y is approximately 11.9 units.