Question

what is the area of triangle def? round to the nearest tenth of a square unit. 10.3 square units 18.0 square units 20.0 square units 20.6 square units trigonometric area formula: area = $\frac{1}{2}absin(c)$

Explanation:

Step1: Identify the values of a, b and C

Let \(a = 5\), \(b = 8\), and \(C=116^{\circ}\)

Step2: Substitute values into the formula

Area \(=\frac{1}{2}ab\sin(C)=\frac{1}{2}\times5\times8\times\sin(116^{\circ})\)

Step3: Calculate \(\sin(116^{\circ})\)

\(\sin(116^{\circ})\approx0.8988\)

Step4: Calculate the area

Area \(=\frac{1}{2}\times5\times8\times0.8988 = 4\times5\times0.8988= 17.976\approx18.0\)

Answer:

18.0 square units