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Answer :
Final answer:
The area of the triangle is calculated using the formula involving the product of the lengths of two sides and the sine of the included angle. The area is approximately 137.5 square units; however, this value is not an exact match with any of the given options.
Explanation:
The area of a triangle with sides of lengths 15, 26, and an included angle of 45 degrees can be calculated using the formula for the area of a triangle when two sides and the included angle are known: Area = ½ × side1 × side2 × sin(included angle). Using this formula, we get: Area = 0.5 × 15 × 26 × sin(45 degrees) = 0.5 × 15 × 26 × 0.7071 (since sin(45 degrees) = √ 2/2). Thus, the area is approximately 137.5 square units. However, none of the answer choices exactly match this value, so we need to recheck the calculation for any rounding errors, but based on the given data and standard trigonometric values, this is the method to use for finding the correct area.
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