Question

Can someone figure this out???

Answer 1

Gotta go so I'll be quick. The Law of Cosines can be solved for the cosine of the angle like this:

`c^2 = a^2 + b^2 - 2 ab \cos C`

`2ab \cos C = a^2 + b^2 - c^2`

`\cos c = (a^2 + b^2 -c^2)/(2 a b)`

We see something like the Pythagorean Theorem in the numerator. When that is zero we have a right triangle with right angle C and hypotenuse c. If that numerator is positive, so is the cosine, so we have an acute angle at C. If that numerator is negative we have an obtuse angle at C.

So we just compute the squares of the sides and the signs of the cosine. Let's divide by nine to keep the numbers small (that won't change the angles) and label a=36/9=4, b=27/9=3, c=45/9=5.

That makes it easy. We don't have to evaluate the cosines. This is just a 3/4/5 right triangle with right angle opposite the 45 side.

Answer 2

Your answer would be a right triangle. Because in the corner there is a 90° angle in the corner of the triangle.

Hope this helps-Aparri

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