What is the area of a triangle with side lengths of 7 and 10, with an included angle of 95º rounded to the nearest hundredth?

To find the area of a triangle when you know two side lengths and the included angle, you can use the formula:

[

\text{Area} = \frac{1}{2}ab \sin(C)

]

where ( a ) and ( b ) are the lengths of the two sides and ( C ) is the included angle between those sides. In this problem, the side lengths are 7 and 10, and the included angle is 95 degrees.

First, plug in the values into the formula:

[

\text{Area} = \frac{1}{2} \times 7 \times 10 \times \sin(95^\circ)

]

Calculating the product of the sides:

[

\frac{1}{2} \times 7 \times 10 = 35

]

Next, calculate (\sin(95^\circ)). Using a calculator, we can find that (\sin(95^\circ) \approx 0.9962).

Now, combine these results:

[

\text{Area} = 35 \times 0.9962 \approx 34.87

]

When rounding this value to the nearest