Question of the week for 10/5/12 to 10/12/12

[XLBC21215]

Question of the week for this week is:

A right triangle has a right angle that measures as 90 degrees. There are sides A, B, and C; where A is the legs, B is the base, and C is our hypotenuse. The right angle is labeled X. Above that angle is Y, and the last one is Z. Since X is 90 degrees, determine that value of angles Y and Z when A=3, and B=4. You may use a calculator.

I will post the answer next Friday .

[XLBC21215]

Sorry I am late with the answer.

First, to find the hypotenuse, we would use the Pythagorean Theorem:

A²+B²=C²

(3)²+(4)²=X²

9+16=X²

25=X²

Square root 25 is 5, so C=5.

Now I will find angle Y. I'll use the trigonometric function COS.

COS Y= ADJACENT/HYPOTENUSE

COS Y= 3/5

COS^-1(.60)=53 degrees (to nearest whole)

So we know that there are 180 degrees in a right triangle. Angle X is 90 degrees (half), and angle Y is 53. The sum of angles X, Y, and Z is 180. Instead of using a trigonometric ratio to find Z, I will write an equation: X+Y+Z=180.

(90)+(53)+Z=180

143+Z=180

Z=37 degrees.

So our solution is: Angle X=90, angle Y=53, and angle Z=37.