SOLUTION: In a right triangle ABC, angle C = 90, c=3, and (a+b)^2=17. Compute the area of the triangle.

Algebra ->  Trigonometry-basics -> SOLUTION: In a right triangle ABC, angle C = 90, c=3, and (a+b)^2=17. Compute the area of the triangle.       Log On


   

Question 1152767: In a right triangle ABC, angle C = 90, c=3, and (a+b)^2=17. Compute the area of the triangle.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

In a right triangle ABC,
angle C+=+90+
c=3
%28a%2Bb%29%5E2=17


the area of the triangle is: A=%281%2F2%29a%2Ab
using Pythagorean theorem,
a%5E2%2Bb%5E2=c%5E2
a%5E2%2Bb%5E2=9.......eq.1
%28a%2Bb%29%5E2=17
a%5E2%2B2ab%2Bb%5E2=17
a%5E2%2Bb%5E2=17-2ab.....eq.2
from eq.1 and eq.2 we have
9=17-2ab....solve for a
2ab=17-9
2ab=8
ab=4.......eq.1a
go to
the area of the triangle is: A=%281%2F2%29a%2Ab, substitute ab
A=%281%2F2%294
A=2