HOW TO FIND AREA OF TRIANGLE WITH TWO SIDES AND ONE ANGLE

Problem 1 :

Find the area of 

Solution :

Let a = 11 cm, b = 15 cm θ = 28°

Area of triangle = 1/2 ab sin θ

= (1/2) ⋅ 11 ⋅ 15 ⋅ sin 28

= (1/2) ⋅ 11 ⋅ 15 ⋅ (0.4694)

= 38.73 cm²

Problem 2 :

Find the area of 

Solution :

Let a = 7.3 km, b = 9.4 km and θ = 38°

Area of triangle = 1/2 ab sin θ

= (1/2) ⋅ 7.3 ⋅ 9.4 ⋅ sin 38

= (1/2) ⋅ 7.3 ⋅ 9.4 ⋅ (0.6156)

= 21.12 km²

Problem 3 :

Find the area of triangle with sides 11 cm, 9 cm and included angle 65°

Solution :

Let a = 11 cm, b = 9 cm and θ = 65°

Area of triangle = 1/2 ab sin θ

= (1/2) ⋅ 11 ⋅ 9 ⋅ sin 65°

= (1/2) ⋅ 11 ⋅ 9 ⋅ (0.9063)

= 44.86 cm²

Problem 4 :

A triangle has sides of length 7 cm and 13 cm and its area is 42 cm². Find the size of its included angle.

Solution :

Let a = 7 cm, b = 13 cm and area = 42 cm²

Area of triangle = 1/2 ab sin θ

42 = (1/2) ⋅ 7 ⋅ 13 ⋅ sin θ

42 = (1/2) ⋅ 7 ⋅ 13 ⋅ sin θ

sin θ = 84 / (7 ⋅ 13)

sin θ = 0.9230

θ = sin^-1(0.9230)

θ = 67.36

Problem 5 :

Find the value of x, if the area is 80 cm². 

Solution :

Area of triangle = 1/2 ab sin θ

80 = (1/2) ⋅ 19.2 ⋅ 11.3 ⋅ sin x

80 = (1/2) ⋅ 216.96 ⋅ sin x

80 = 108.48 ⋅ sin x

sin x = 80/108.48

sin x = 0.7374

x = sin^-1(0.7374)

x = 47.5 cm

Problem 6 :

Solution :

Area of triangle = 1/2 ab sin θ

= (1/2) ⋅ 7 ⋅ 7 ⋅ sin (13π/18)

= (49/2) ⋅ (0.766)

= 18.767 cm²