Question 1062981
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A triangular bench is modeled by △ABC, in which m∠C=50°, AC=3.5, AB=2.81, and BC=1.4.

https://cds.flipswitch.com/tools/asset/media/576477

Wayra must buy enough fabric to cover the entire bench.

Assuming the given measurements are in yards, how much fabric must he buy?

Approximately __________ square yards of fabric are needed.
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<pre>
The area of a triangle is the half of the product of two its side lengths by the sine of the angle concluded between the sides:


S = {{{(1/2)*abs(AC)*abs(BC)*sin(C)}}} = {{{(1/2)*3.5*1.4*sin(50^o)}}}.


Use your calculator.


The length of AB is excessive data. 
It is not needed to solve the problem.
</pre>

On area of triangles see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Surface-area/Formulas-for-area-of-a-triangle.lesson>Formulas for area of a triangle</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Surface-area/-Proof-of-the-Heron%27s-formula-for-the-area-of-a-triangle.lesson>Proof of the Heron's formula for the area of a triangle</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Surface-area/One-more-proof-of-the-Heron%27s-formula-for-the-area-of-a-triangle.lesson>One more proof of the Heron's formula for the area of a triangle</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Surface-area/Proof-of-the-formula-for-the-area-of-a-triangle-via-the-radius-of-the-inscribed-circle.lesson>Proof of the formula for the area of a triangle via the radius of the inscribed circle</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Surface-area/Proof-of-the-formula-for-the-radius-of-the-circumscribed-circle.lesson>Proof of the formula for the radius of the circumscribed circle</A> 


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-area-of-triangles.lesson>Solved problems on area of triangles</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-area-of-right-angled-triangles.lesson>Solved problems on area of right-angled triangles</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-area-of-regular-triangles.lesson>Solved problems on area of regular triangles</A>  

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-the-radius-of-inscribed-circles-and-semicircles.lesson>Solved problems on the radius of inscribed circles and semicircles</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-the-radius-of-a-circumscribed-circle.lesson>Solved problems on the radius of a circumscribed circle</A>  

in this site.


Also, &nbsp;you have this free of charge online textbook on Geometry

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson>GEOMETRY - YOUR ONLINE TEXTBOOK</A> 

in this site.


The referred lessons are the part of this online textbook under the topic "<U>Area of triangles</U>".