SOLUTION: Find the area of the triangle. Round your answer to the nearest tenth. https://www.webassign.net/waplots/9/f/0f28e6639bfdd603f95c8270025672.gif

Algebra ->  Trigonometry-basics -> SOLUTION: Find the area of the triangle. Round your answer to the nearest tenth. https://www.webassign.net/waplots/9/f/0f28e6639bfdd603f95c8270025672.gif      Log On


   

Question 1204655: Find the area of the triangle. Round your answer to the nearest tenth.
https://www.webassign.net/waplots/9/f/0f28e6639bfdd603f95c8270025672.gif
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

SAS is Side, Angle, Side
Given the size of 2 sides (c and a) and the size of the angle B that is in between those 2+sides you can calculate the sizes of the remaining 1+side and 2 angles.

c=7
a=6
angle B=59

use The Law of Cosines to solve for the remaining side, b
b%5E2+=+a%5E2+%2B+c%5E2+-+2ca%2Acos%28B%29
b%5E2+=+6%5E2+%2B+7%5E2+-+2%2A7%2A6%2Acos%2859%29
b%5E2+=+36+%2B+49+-+43.26319829244455
b%5E2=41.73680170755545
b=sqrt%2841.73680170755545%29
b=6.5

to calculate area, we need semi-perimeter first

Triangle perimeter, P+=+a+%2B+b+%2B+c=6%2B6.5%2B7=19.5
Triangle semi-perimeter, s+=+%281%2F2%29%2A+%2819.5%29=9.75

Then triangle area is:
A+=+sqrt%28s%2A%28s-a%29%2A%28s-b%29%2A%28s-c%29%29
A+=+sqrt%289.75%2A%289.75-6%29%2A%289.75-6.5%29%2A%289.75-7%29%29
A=18.07698381229568
A=18.1



Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the area of the triangle. Round your answer to the nearest tenth.
https://www.webassign.net/waplots/9/f/0f28e6639bfdd603f95c8270025672.gif
~~~~~~~~~~~~~~~~~~~ 

You are given the lengths of two sides of a triangle and the angle between them.


With this given data, the area of the triangle is half-product of the side lengths
and the sine of the angle between them. So the area at given condition can be computed in one line

    area = %281%2F2%29%2A6%2A7%2Asin%2859%5Eo%29 = %281%2F2%29%2A6%2A7%2A0.8571673 = 18.00 square units  (rounded).   ANSWER

Solved.

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On different formulas for a triangle area see the lesson
    - Formulas for area of a triangle
in this site.

In this concrete case,  I recommend using the simplest formula above in my post
and  DO  NOT  USE  more complicated formulas.

Using over-complicated formulas for simple problems like this one is demonstration
of mathematical illiteracy and definitely is  WRONG  TEACHING.

I do not think that your goal is to demonstrate your mathematical incompetence to all people around.


Happy learning (!)