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?

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?

• A. 34.87 square units
• B. 30.25 square units
• C. 28.76 square units
• D. 36.5 square units

Answer: (A)

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

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