This post uses trigonometric functions in Excel to analyze the area of right triangles with different angles.
Question: I have a string of 25 inches, which I use to make right triangle ABC. AB and BC are the sides and AC the hypotenuse. Angle ABC is 90 degrees. Angle BCA ranges from 5 to 85 in increments of 5. Angle BAC is 90-angle BCA.
Calculate the area of the right triangles defined by angle BCA.
Analysis: Denote the hypotenuse as X.
Line Segment AB is the Sine(BCA)*X.
Line Segment BC is the Cos(BCA)*X.
The perimeter is 25 = X +X*Sine(BCA) + X*COS(BCA)
The COSINE and SINE are known from the angle.
Solve for X.
X=25/(1 + Cos + Sine)
The calculation of the hypotenuse is outlined below.
After finding X find length of segments AB and BC from formulas.
The area is AB*BA*.5.
Observation: Note that the triangle with angle BCA equal to a is identical triangle with BCA equal to 90-a because BCA and BAC must sum to 90 and the two triangles are flipped.