The hypotenuse of a 30°-60°-90º triangle is 8 units and one leg is 4 units. What is the length of the other leg?

The length of the other leg is

Step-by-step explanation:

There are 2 ways to solve this.

1) Pythagorean theorem (the harder way)

A 30-60-90 triangle is a right triangle, and therefore you can use the pythagorean theorem to calculate the measure of 1 side given the 2 others.

That's one solution, but its not a very nice number or the exact answer you probably want. Instead, you can simplify the root.

First, you need to factor 48:

The prime factors of 48 are:

Then, you need to find perfect squares:

And finally, you can remove those like this:

The length of the other leg is

2) 30-60-90 triangle relationships (the easier way)

There are 4 simple rules here:

They're actually pretty easy to remember. You can multiply the short leg by 2 or √3, and 2 is greater than √3 (check a calculator). The hypotenuse of course is also longer than the long leg, so you have to multiply by 2 to get it. Then for the long leg, the only option is to multiply by √3. The same works in reverse for both of those.

Here, we have the short leg. You can check that with the pythagorean theorem again to be sure:

Because 16 is less than half of 64, a has to be the longer leg. Using the rules above, multiply the short leg by √3 to get the

Same answer as the previous method.

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.

10

step-by-step explanation:

7+3=10