If sides A and B of a triangle have lengths of 6 and 12 respectively, and the angle between them is (pi)/8, then what is the area of the triangle?

3 Answers
May 31, 2018

Area of the triangle is 13.78 sq.unit.

Explanation:

Angle between Sides A and B is

/_c= pi/8=180/8=22.5^0. Sides are A=6 , B=12

Area of the triangle is A_t=(A*B*sin c)/2 or

A_t=(6*12*sin 22.5)/2~~ 13.78 sq.unit

Area of the triangle is 13.78 sq.unit [Ans]

May 31, 2018

text{area} = 1/ 2 a b sin C = 1/2 (6)(12) sin (pi/8) = 18 sqrt{2-sqrt{2}}

Explanation:

sin(pi/8) = sin(45^circ/2) = sqrt{1/2(1 - cos 45^circ)} =sqrt(1/2(1-sqrt{2}/2)) = 1/2 sqrt{2 - sqrt{2}}

13.8

Explanation:

Let's plot this triangle on an imaginary two-dimensional graph so that:

Your given angle (we can call it theta) is located at the origin, with line A on the x axis and line B slanting upwards and rightwards at the angle pi/8 from the origin.

We can now calculate the y-component of line B as 12*sin(theta) which is approximately 4.6 units.

We can now multiply the 'base' of the triangle (A) by the 'height' of the triangle (b_y) and we get 6*4.6 = 27.6. Halve that and you get your area.