Questions: Find the area of the triangle below. Carry your intermediate computations to at least four decimal places. Round your answer to the nearest hundredth.

Find the area of the triangle below. Carry your intermediate computations to at least four decimal places. Round your answer to the nearest hundredth.
Transcript text: Find the area of the triangle below. Carry your intermediate computations to at least four decimal places. Round your answer to the nearest hundredth.
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Solution

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Solution Steps

Step 1: Find the height of the triangle

We can use the trigonometric function sine to find the height (h) of the triangle. We know the hypotenuse (6 ft) and the angle (50°).

sin(50°) = h / 6 ft

h = 6 ft * sin(50°)

h ≈ 6 ft * 0.7660

h ≈ 4.596 ft

Step 2: Calculate the area

The area of a triangle is given by the formula:

Area = (1/2) * base * height

In this case, the base is 10 ft and the height we calculated is approximately 4.596 ft.

Area ≈ (1/2) * 10 ft * 4.596 ft

Area ≈ 22.98 ft²

Final Answer:

22.98 ft²

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