Question 581739: Find the area of a scalene triangle (no 90 degree angle ) without using any
trigonometry fucntion when you are given: side a, b, c.
Please grade the difficulty of this problem.
Thank you. R. Bommarito.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the area of a scalene triangle (no 90 degree angle ) without using any
trigonometry function when you are given: side a, b, c.
Please grade the difficulty of this problem.
Thank you. R. Bommarito.
**
Given a scalene triangle with sides a, b, and c, designate one of the sides(c) as the base, then draw a perpendicular line from this base up to the apex. This line is the height(h) and it breaks the original triangle into two right triangles with the base split into two parts. Call one part x and the other part c-x. You can solve for h with two separate equations using the pythagorean Theorem as follows:
h^2=a^2-x^2
h^2=b^2-(c-x)^2=b^2-c^2+2cx-x^2
set equations equal to each other
a^2-x^2=b^2-c^2+2cx-x^2
a^2-b^2+c^2=2cx
x=a^2-b^2+c^2/2c
h^2=a^2-x^2
h=√(a^2-x^2)
Area of triangle=1/2 base*height
On a scale of 1 to 4,I would give it a rating of 3 for difficulty.
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