Geometry Help!!

Question

Patrick is practicing his aim in golf. His brother tells him that the angle he hits the ball at is  degrees to his right and that the distance the ball travels, to point , is equal to  yards. He was aiming for point .

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What is the distance he should have hit the ball?

 __________ 

Answer 1

In this problem, you have a special Right Triangle. Therefore, each of the 2 other angles are each 45 degrees.

We know that from this situation, the Hypotenuse is found by multiplying one of the sides by the square-root of 2.

Since we already have the Hypotenuse value as 8 x Square root of 2, then by dividing this figure by the square root of 2, we have our answer, which is 8 yards.

Patrick was aiming for Point B but instead hit the ball to Point C. We know this distance to be 8 x Square-root of 2 (The hypotenuse).

Answer is: He should have hit the ball 8 Yards to Point B.

Answer 2

What kind of triangle is this? It's a right triangle because of the 90° angle, and the 45° angle tells me this is a 45-45-90 right triangle, which is a SPECIAL right triangle! You have the length of the longest side (hypotenuse) and want to know the length of the shorter side "c".

In a standard 45-45-90 special right triangle, the sides are length 1 for both of the smaller sides and length √2 for the hypotenuse (longest side). Our triangle, though, has been MAGNIFIED to be way bigger! So the standard side lengths 1 (short side), 1 (short side), and √2 (longest side) have all been multiplied by something!

Let's figure out how much bigger all of the sides are. If the hypotenuse (longest side) is usually length √2, but in our problem it's magnified to be length 8√2, that means it has been multiplied by a factor of 8. So that means ALL of the sides of my standard 45-45-90 special right triangle are multiplied by 8. So instead of my standard lengths 1, 1, √2, I have 1 * 8, 1 * 8, and 8 * √2, or 8, 8, 8√2. So the lengths of the shorter sides of this magnified triangle are BOTH 8, and the missing side "c" must be 8 yards long.