In a DeltaABC, b=10m, c=21m and /_A=58^o. What is the area of the triangle?

(a) $105$ ${m}^{2}$ (b) $55.64$ ${m}^{2}$ (c) $82.02$ ${m}^{2}$ (d) $89.05$ ${m}^{2}$

Jun 26, 2016

(d) $89.05$.

Explanation:

As $b = 10 m$, $c = 21 m$ and $\angle A = {58}^{o}$

Area of the triangle is given by

$\frac{1}{2} \times b \times c \times \sin A$

= $\frac{1}{2} \times 10 \times 21 \times \sin {58}^{o}$

= $\frac{1}{2} \times 10 \times 21 \times 0.84805$

= $5 \times 21 \times 0.848 = 89.05$ ${m}^{2}$

Hence answer is (d) $89.05$.