Answer:
area = 31 ft^2
Step-by-step explanation:
To start we have to know the law of cosine
Law of Cosines. The law of cosines for calculating one side of a triangle when the angle opposite and the other two sides are known. ... To calculate a or b, first use the law of sines to find the angle opposite the side you wish to calculate. Then use the law of cosines to find the unknown side length.
a^2 = b^2 + c^2 - 2bc cos(A)
a = 35°
b = 11 feet
c = 10 feet
a^2 = 11^2 + 10^2 - (2*11*10*cos (35))
a^2 = 121 + 100 - 220* 0.819
a^2 = 221 - 180
a = √ 41
a = 6.4
Heron's formula finds the area of a triangle of which all its sides are known. The area is calculated from the semiperimeter of the triangle s and the length of the sides (a, b and c).
s = (a+b+c)/2
s = ( 6.4 + 11 + 10)/2
s = 27.4/2
s = 13.7
√ (s(s-a)(s-b)(s-c))
we replace the formula and solve
√ (13.7(13.7 - 6.4)(13.7 - 11)(13.7 - 10))
√ (13.7(7.3)(2.7)(3.7))
√999
31.6
area = 31.6 ft^2
