Question

The lengths of the sides of a triangle are square root 139, square root 73, and 6. Classify the trianglo as “acute", "right", or "obtuso".

Choose the correct type of triangle below.
O acute
obtuse
Oright

Answer 1

It's obtuse.

Explanation:

Mumble. Smells al-kashi laws of cosine to me.

`a^2-b^2-c^2 = -2bc cos\alpha\\b^2-c^2-a^2=-2ca cos \beta\\c^2-a^2-b^2=-ab cos \gamma`

Now, we don't need to calculate the RHSs, and then:

If at least one of the three LHSs is greater than zero, the triangle is obtuse

If at least one is zero, it's a right triangle (pythagorean theorem anyone?)

if all three numbers are less than zero, the triangle is acute

Start crunching numbers.

`139-73-36 = 30` First try was the charm. finding 30 means that the product
`[-2(√(73))(6) ]cos \alpha` is positive, and since the product in the large bracket is negative, the cosine has to be 0, thus the angle has to be greater than 90°, QED