Question

find the area of this triangle.
5
110°
7
? square units
round to the nearest hundredth.

Explanation:

Step1: Recall the formula for the area of a triangle with two sides and included angle

The formula is \( A = \frac{1}{2}ab\sin C \), where \( a \) and \( b \) are the lengths of two sides, and \( C \) is the included angle between them.
Here, \( a = 7 \), \( b = 5 \), and \( C = 110^\circ \).

Step2: Substitute the values into the formula

First, calculate \( \sin(110^\circ) \). Using a calculator, \( \sin(110^\circ) \approx 0.9397 \).
Then, substitute into the formula: \( A = \frac{1}{2} \times 7 \times 5 \times \sin(110^\circ) \).

Step3: Perform the calculation

First, calculate \( \frac{1}{2} \times 7 \times 5 = \frac{35}{2} = 17.5 \).
Then, multiply by \( \sin(110^\circ) \): \( 17.5 \times 0.9397 \approx 16.44475 \).

Step4: Round to the nearest hundredth

Rounding \( 16.44475 \) to the nearest hundredth gives \( 16.44 \).

Answer:

\( 16.44 \)