Monday, July 18, 2011

The Problem of the Week Day 1: Week of 7/17 - 7/23

The problem of the week is back for its second time! Make sure you did last month's problem because the answers are going up this Saturday. Don't forget to round to the nearest tenth unless told otherwise.

Easy Problem: Last month, we learned about the Pythagorean Theorem and how to figure out the missing side of a right triangle. Just to refresh your memory, the square of the longest side: c, equals the sum of the squares of the two shorter sides, a and b. So, a^2 + b^2 = c^2.

If you were missing a and b, it is just another algebra equation, but the inverse operation to squaring is square rooting.

If you have a right triangle with a =12 and c = 20, what does b equal?

b = ___

Hard Problem: Last month, we learned about the sine function. Now, we will look at another function that you might not have on your average calculator, but if you hit the 2nd button on a scientific calculator or iPhone calculator, you will get a button where the sine function has a little -1 above it, in the place of an exponent. That button takes the sine of an angle, and turns it into the angle. So, you could divide the side opposite to an angle by c and get the sine, and then hit that button to retrieve your angle.

If a right triangle had a = 6 inches, b = 8 inches and c = 10 inches, what would the two missing angles be? The angle opposite of a will be called t and the angle opposite of b will be called s.

s = ____
t = ____

Tip: Every triangle, right or not, is guaranteed to have its angles sum up to 180° if on a flat surface. Therefore, you only need to use trigonometry for one angle, and use arithmetic for the other.