Question

Find the area of this triangle
8
123 degrees
15

Answer 1

50.32 square units

Explanation:

To find the area of a triangle, given the measures of two of its side lengths and the included angle, use the Sine Rule.

`\boxed{\begin{minipage}{6 cm}\underline{Sine Rule - Area of a triangle} \\\\$A=(1)/(2)ab \sin C$\\\\where:\\ \phantom{ww}$\bullet$\;\;$a$ and $b$ are the sides.\\ \phantom{ww}$\bullet$\;\;$C$ is the incl\:\!uded angle. \\\end{minipage}}`

From inspection of the given triangle:

• a = 8
• b = 15
• C = 123°

Substitute these values into the formula and solve for A:

`\begin{aligned}A&=(1)/(2) \cdot 8 \cdot 15 \cdot \sin 123^(\circ)\\\\&=4 \cdot 15 \cdot \sin 123^(\circ)\\\\&=60 \cdot \sin 123^(\circ)\\\\&=50.3202340...\\\\&=50.32\; \sf square\;units\;(nearest\;hundredth)\end{aligned}`

Therefore, the area of the given triangle is 50.32 square units (rounded to the nearest hundredth).