Question

1. Write out the law of cosines and find the hypotenuse of triangle with 2 sides lengths equal to three and the included angle measuring 75 degrees.

2. What happens in law of cosines formula if the angle from the above question is changed to 90 degrees.

Answer 1

1.)
`√(13.341)` ≈ 3.652

2.) I would say something about how the A in front of cos in the equation would change to 90, rather than stay 75 (in the equation for the step by step), but it would be easier to just use the Pythagorean theorem.

Explanation:

I think we may have the same class so hopefully this helps:

1.)
`a^2 = b^2 + c^2 - 2bccosA` --> law of cosines formula.

`a^2 = 3^2 + 3^2 - 2(3)(3)cos(75)` --> plugged in numbers; when you draw the triangle, the included angle would be A, and the opposite side would be a. B and b, and C and c are opposite each other. In this case, a is the hypotenuse.

`a^2 = 18 - 18cos75` --> in between steps.

`a^2 = 13.341` --> more simplifying.

`a(hypotenuse) = √(13.341) or 3.652` --> answer

2.) This one is just an explanation: The 75 in the equation is the given angle, which is a. If this changes, it would just change in the equation too. And obviously, if it's 90 degrees, you can just use Pythagorean theorem a^2+b^2=c^2.

Good luck! :)