Question

what is the area of triangle pqr? round to the nearest tenth of a square unit.
70.5 square units
111.3 square units
185.4 square units
222.5 square units
trigonometric area formula: area = $\frac{1}{2}absin(c)$

Explanation:

Step1: Identify the values of a, b and C

Let \(a = 20\), \(b=12\) and \(C = 36^{\circ}\)

Step2: Substitute values into the formula

Area \(=\frac{1}{2}\times20\times12\times\sin(36^{\circ})\)
First, calculate \(\frac{1}{2}\times20\times12 = 120\)
Then, find \(\sin(36^{\circ})\approx0.5878\)
Area \(=120\times0.5878 = 70.536\)

Step3: Round the result

Rounding \(70.536\) to the nearest tenth gives \(70.5\)

Answer:

70.5 square units