SOLUTION: The lengths of the sides of a non-right triangle are 17 inches, 9 inches, and 12 inches. Find the area of the triangle. Round to the nearest tenth.

Question 132782This question is from textbook Fundamentals of Algebric Modeling
: The lengths of the sides of a non-right triangle are 17 inches, 9 inches, and 12 inches. Find the area of the triangle. Round to the nearest tenth.This question is from textbook Fundamentals of Algebric Modeling

Found 2 solutions by Earlsdon, solver91311:
Answer by Earlsdon(6103) (Show Source):
You can put this solution on YOUR website!
Use Heron's formula to find the area of a triangle when only the lengths of the sides are known.

S is the semi-perimeter of the triangle
A, B, and C are 17, 9, and 12 respectively, the lengths of the sides of the triangle.
Let's find S, the semi-perimeter.

Now to find the area:

Round to the nearest tenth.
sq. ins.

Answer by solver91311(12126) (Show Source):
You can put this solution on YOUR website!
TRIANGLE SOLUTION

Given: 'a' = 9, 'b' = 17, 'c' = 12

1. Use the Cosine Rule to calculate
the largest angle: 'B'

so
degrees

2. Use the Sine Rule to find one of
the two remaining angles, eg angle 'C'

3. Calculate angle 'A'

Summary
sides: a=9, b=17, c=12
angles: A=30.3738°, B=107.235°, C=42.3909°

Calculations:
AREA = (base × perpendicular height) / 2

Let side 'c' be the base,

then the perpendicular height = 'b' × sin(A)
= 17 × sin(30.3738)
= 8.59586
so area = ( 12 × 8.59586 ) / 2
= 51.5752 or to the nearest 10th, 51.6