Expert: Sherman D. - 2/27/2006

Question
Good morning,

I have a right triangle.  I know the angles of all three sides

The right angle is on the right side.  The top angle is 20 degrees and the one to the left of the right angle is 70 degrees.  I know that the line between the right angle and the 70 degree angle is 8 inches.  I am trying to find the lenght of the other two lines.


Answer
Using 70°

Tan(70°) = x/8
x = 8Tan(70°)
x = about 22 inches

Cos(70°) = 8/y
y = 8/(cos(70°))
y = about 23 inches

--------------------------------

Using 20°

Tan(20°) = 8/x
x = 8/Tan(20°)
x = about 22 inches

Sin(20°) = 8/y
y = 8/(sin(20°))
y = about 23 inches

Proof

Using a^2 + b^2 = c^2

(8/(tan(20°)))^2 + 8^2 = (8/(sin(20°)))^2
483.1125 + 64 = 547.1125
547.1125 = 547.1125

or

(8Tan(70°))^2 + 8^2 = (8/(cos(70°)))^2
483.1125 + 64 = 547.1125
547.1125 = 547.1125