find the area of the given triangle. round your answer to the nearest tenth. do not round any intermediate…

Explanation:

Step1: Identify triangle type and sides

The triangle is right - angled. One leg (let's say adjacent to the 39° angle) is 10. Let the other leg (opposite to 39° angle) be (y). We can use the tangent function: (\tan(39^{\circ})=\frac{y}{10}), so (y = 10\times\tan(39^{\circ})).

Step2: Calculate the other leg

(\tan(39^{\circ})\approx0.8098), so (y = 10\times0.8098 = 8.098).

Step3: Calculate the area of the right - triangle

The area of a right - triangle is (A=\frac{1}{2}\times base\times height). Here, base = 10 and height = (y = 8.098). So (A=\frac{1}{2}\times10\times8.098=5\times8.098 = 40.49).

Step4: Round to the nearest tenth

Rounding 40.49 to the nearest tenth gives 40.5.

Answer:

40.5