Question

Find the area of the triangle. Round your answer to one decimal place. 

C = 103° 15' a = 18, b = 25

Answer 1

Area of a triangle:

Let \(a\) and \(b\) be two sides of a triangle and \(C\) be the angle between them.

$$ \text { Then } \text { Area of the triangle }=\frac{1}{2} a b \sin C $$

17. Given: \(a=18, \quad b=25\),

$$ C=103^{\circ} 15^{\prime}=\left(103+\frac{15}{60}\right)^{\circ}=103.25^{\circ} $$

Hence the area of the tringle is

$$ \begin{aligned} \frac{1}{2} a b \sin C &=\frac{1}{2} \times 18 \times 25 \times \sin 103.25^{\circ} \\ &=9 \times 25 \times 0.973379258 \\ &=219.01 \end{aligned} $$

\(=219 \quad\) (Round to one decimal place)

Area \(=219\)