Answer:
To find the area of the given triangle, we can use the formula for the area of a triangle when two sides and the included angle are known:
\(\[ \text{Area} = \frac{1}{2}ab\sin(C) \]\)
where:
- \( a \) and \( b \) are the lengths of two sides.
- \( C \) is the included angle between those sides.
In this case:
- \(\( a = 6 \)\) cm
- \(\( b = 11 \)\) cm
- \(\( C = 53^\circ + 26^\circ = 79^\circ \)\)
Now, calculating the area:
\(\[ \text{Area} = \frac{1}{2} \times 6 \text{ cm} \times 11 \text{ cm} \times \sin(101^\circ) \]\)
First, find the sine of \(\(101^\circ\)\):
\(\[ \sin(101^\circ) \approx 0.9816 \]\)
Then, calculate the area:
\(\[ \text{Area} = \frac{1}{2} \times 6 \times 11 \times 0.9816 \]\)
\(\[ \text{Area} = \frac{1}{2} \times 6 \times 11 \times 0.9816 \]\)
\(\[ \text{Area} = 33 \times 0.9816 \]\)
\(\[ \text{Area} \approx 32.393 \]\)
Rounded to 1 decimal place, the area is approximately:
\(\[ \text{Area} \approx 32.4 \text{ cm}^2 \]\)
Step-by-step explanation:
