Question

Find the area of △ABC with side lengths a = 13 and b = 7, and included angle C = 65°. Round your answer to the nearest tenth.

A) 23.4 square units

B) 45.5 square units

C) 37.5 square units

D) 19.8 square units

Answer 1

The area of triangle ABC with sides a = 13, b = 7, and included angle C = 65°, when calculated and rounded to the nearest tenth, is approximately 41.1 square units. None of the provided answer choices match this result.

Step-by-step explanation:

To find the area of triangle ABC with sides a = 13 and b = 7, and included angle C = 65°, we can use the formula for the area of a triangle when two sides and the included angle are known: Area = 1/2 × a × b × sin(C). Plugging the values into the formula:

Area = 1/2 × 13 × 7 × sin(65°)

First, calculate the sine of 65° using a calculator.

sin(65°) ≈ 0.9063

Now, substitute this value into the formula:

Area = 1/2 × 13 × 7 × 0.9063 ≈ 41.105

Rounding the result to the nearest tenth gives an area of approximately 41.1 square units. This answer is not listed in the provided options, suggesting a potential mistake in the options or the need for reevaluation of the initial information.