Question

right triangle relationships and trigonometry
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

Explanation:

Step1: Recall the formula for the area of a triangle

The formula for the area of a triangle is \(A=\frac{1}{2}ab\sin(C)\), where \(a\) and \(b\) are two sides of the triangle and \(C\) is the included angle.

Step2: Identify the values of \(a\), \(b\), and \(C\)

Here, \(a = 12\), \(b=20\), and \(C = 68^{\circ}\)

Step3: Substitute the values into the formula

\(A=\frac{1}{2}\times12\times20\times\sin(68^{\circ})\)
First, calculate \(\frac{1}{2}\times12\times20= 120\)
Then, find \(\sin(68^{\circ})\approx0.9272\)

Step4: Calculate the area

\(A = 120\times0.9272=111.264\approx111.3\)

Answer:

111.3 square units