Question

find the area of the triangle described below. round to the nearest hundredth.

b = 41^{circ}, a = 15, c = 22

Explanation:

Step1: Recall the formula for the area of a triangle

The formula for the area of a triangle when two sides \(a\), \(c\) and the included angle \(B\) are known is \(A=\frac{1}{2}ac\sin B\).

Step2: Substitute the given values into the formula

We are given \(a = 15\), \(c=22\), and \(B = 41^{\circ}\). First, we need to find the value of \(\sin(41^{\circ})\). Using a calculator, \(\sin(41^{\circ})\approx0.6561\).
Then substitute into the formula: \(A=\frac{1}{2}(15)(22)(0.6561)\).
First, calculate \(\frac{1}{2}(15)(22)\): \(\frac{1}{2}(15)(22)= 15\times11 = 165\).
Then multiply by \(\sin(41^{\circ})\): \(A=165\times0.6561\).

Step3: Calculate the final value

\(A = 165\times0.6561=108.2565\)

Answer:

\(108.26\)