Question

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

Answer 1

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

Answer 2

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