Find the area of the triangle?

Question

Find the are of the triangle in which b=249, c=372, A=56degrees22'

Answer 1

Here height c = 372 and b = 249 and A = 56°.22'

The right angle triangle of the area is (1/2)(bh sinθ)

area = (1/2)(249)(372)sin(56°.22')

Trigonometry table in sin(56°.22') = 0.8311

area = (1/2)(92628)(0.8311)

area = 38491.565 square units.

There fore the area of triangle is 38491.565 square units.

Comments

Area of an oblique triangle :

The area of any triangle is one - half the product of the lengths of two sides times
the sine of their included angle. That is,
Area = (1/2)bc sin A = (1/2)ab sin C = (1/2)ac sin B.

Note : If angle A is 90⁰ , the formula gives the area for a right triangle :

Area = (1/2)bc sin (90⁰) = (1/2) * b * c * (1) = (1/2) * base * height.

Similar results are obtained for angles C and B equal to 90⁰.

 

From the given data, draw the right triangle with given measurements.

Here height c = 372 and b = 249 and A = 56°.22'.

Area of the oblique triangle with angle is (1/2)(bc sinA).

Area = (1/2)(249)(372)sin(56°.22')

From trigonometry table : sin(56°.22') = 0.8326.

Area = (249)(186)(0.8326)

area = 38561.0364 square units.

Therefore, the area of triangle is 38561.0364 square units.