Brianna made a design with chalk on the playground in the shape of a triangle. Two sides of the triangle measuring 5 feet and 8 feet meet at a 40° angle. What is the area of the triangle? Round your answer to the nearest tenth.

12.9 ft²

Step-by-step explanation:

sin = opp/hyp

sin 40 = height/ 5

5 * sin40 = height

h = 3.213938048432697

--------------------

area = (1/2)bh

a = (1/2) * 8 * 3.213938048432697

a = 12.9 ft²

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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