To the nearest hundredth, what is the area of a triangle with side lengths of 4 and 15 and an included angle of 26º?

To find the area of a triangle when two sides and the included angle are known, you can use the formula:

[

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

]

where ( a ) and ( b ) are the lengths of the sides, and ( C ) is the included angle in degrees.

In this case, the side lengths are 4 and 15, and the included angle ( C ) is 26 degrees. Plugging these values into the formula gives:

[

\text{Area} = \frac{1}{2} \times 4 \times 15 \times \sin(26^\circ)

]

Calculating this step by step:

1. Calculate ( \frac{1}{2} \times 4 \times 15 ):

[

= \frac{1}{2} \times 60 = 30

]

2. Next, find ( \sin(26^\circ) ). Using a calculator, ( \sin(26^\circ) \approx 0.4384 ).

3. Multiply these values together:

[

\text{Area} = 30