Question

A triangle has two sides of lengths 7 cm and 12 cm, and the angle between them is

15°. Find the area of the triangle rounded to two decimal places.

Answer 1

10.80 cm²

Explanation:

C 15°

/ \

/ \

/ \

7/ \ 12

/ \

/ \

/ \

B -----------A

c

a = 7 cm

b = 12 cm

it's not a right triangle, so we CANT use the pythagorean theorem

1. Law of Cosines to find 3rd side

c^2 = a^2 + b^2 - 2ab cos(C)

c^2 = 7^2 + 12^2 - 2(7)(12)cos(15°)

c^2 ≈ 135.81

c ≈ 11.64

2. Get area of a triangle

Area = 1/2 * base * height

C (15°)

/|\

/ | \

/ | \

7/ |h \ b = 12 cm

/ | \

/ | \

/ | \

B -----------A

c =11.64 cm

Law of Sines to find the height

sin(15°) = height / 7

height ≈ 1.80

Area = 1/2 * 12 cm * 1.80 cm ≈ 10.80 cm^2

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