Find the area of the triangle with A = 35°, b = 11 feet, and c = 10 feet. Round to the nearest tenth.

Answer: 31.5ft²

Step-by-step explanation:

For any given triangle with two adjacent sides and an opposing angle, the area is determined by the formula:

1/2 * length A * length B * sin of angle of opposing side.

That is, if lenght A=x, length B = y and opposing angle is given as Z, then the area of such triangle becomes:

Area = 1/2 * x*y*sin Z

For the given triangle, x = 11feet, y = 10feet, Z=35°

Area = 1/2 * 11 * 10 * sin 35

Area = 31.5469ft²

Rounding up to the nearest tenth,

Area = 31.5ft²

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