Question

NVM

Answer 1

For problem s, you can see if you do a little bit of work that the two sides are the same length, and the sum of the squares of their lengths is the square of the length of the hypotenuse. Therefore the answer choice involving the Pythagorean theorem is correct.

Here's how I worked it out:

The two sides both go 7 in one direction and 1 in the other, so we can find the length by the Pythagorean theorem: \(d = \sqrt{7^2 + 1^2} = \sqrt{50} = 5\sqrt{2}\)

The hypotenuse goes 8 units in one direction and 6 in the other, so its length is:\[d=\sqrt{8^2+6^2} = \sqrt{100} = 10\]

We can see that these lengths satisfy the Pythagorean theorem:

\((5\sqrt{2})^2 + (5\sqrt{2})^2 = 25*2 + 25*2 = 50+50 = 10^2 = 100\)

So, this is a right triangle (and an isosceles one, at that).

Answer 2

In #9 in file h, remember the memory aid:

SOH CAH TOA

Sin = Opposite over Hypotenuse
Cos = Adjacent over Hypotenuse
Tan = Opposite over Adjacent

Answer 3

You'll have to give it your best shot...