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.

Algebra ->  Formulas -> 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.      Log On


   

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(6294) About Me  (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.
A+=+sqrt%28S%28S-A%29%28S-B%29%28S-C%29%29
S is the semi-perimeter of the triangle %28A%2BB%2BC%29%2F2
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.
S+=+%2817%2B9%2B12%29%2F2
S+=+38%2F2
S+=+19
Now to find the area:
A+=+sqrt%2819%2819-17%29%2819-9%29%2819-12%29%29
A+=+sqrt%2819%282%29%2810%29%287%29%29
A+=+sqrt%2819%28140%29%29
A+=+sqrt%282660%29
A+=+51.575 Round to the nearest tenth.
A+=+51.6sq. ins.

Answer by solver91311(24713) About Me  (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'
cos%28+B+%29=+%28c%5E2+%2B+a%5E2+-+b%5E2%29%2F%282ca%29
cos%28+B+%29=++%2812%5E2+%2B+9%5E2+-+17%5E2%29%2F%282%2A12%2A9%29
so B+=+cos%5E%28-1%29%28-0.296296%29
B+=+107.235 degrees

2. Use the Sine Rule to find one of
the two remaining angles, eg angle 'C'
%28sin%28+C%29%29%2Fc+=+%28sin%28+B%29%29%2Fb
%28sin%28+C%29%29%2F12+=+%28sin%28+107.235%29%29%2F17
sin%28+C%29+=+12%28sin%28+107.235%29%29%2F17
C+=+sin%5E%28-1%29%28+0.674185%29
C+=+42.3909

3. Calculate angle 'A'
A+=+180+-+%28B%2BC%29
A+++=+180+-+%28107.235+%2B+42.3909%29
A+++=+180+-+149.626
A+++=+30.3738

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