To determine the approximate length of wood needed to trim the window, we need to find the lengths of all three sides of the triangle.
Using the given information, we know that the hypotenuse is 6 ft. We can calculate the length of the remaining two sides using trigonometric ratios.
Let's label the sides of the triangle as follows:
Opposite: x (length of the side opposite the 30-degree angle)
Adjacent: y (length of the side adjacent to the 30-degree angle)
Hypotenuse: 6 ft
We can use the sine and cosine ratios to calculate the lengths of the sides:
Sine ratio: sin(30) = opposite/hypotenuse
sin(30) = x/6
x = 6 * sin(30)
x = 3 ft
Cosine ratio: cos(30) = adjacent/hypotenuse
cos(30) = y/6
y = 6 * cos(30)
y = 6 * (√3/2)
y = 3√3 ft (approximately 5.2 ft when rounded to one decimal place)
Now, to find the approximate length of wood needed to trim the window, we add up the lengths of all three sides:
Total length of wood = x + y + hypotenuse
Total length of wood = 3 ft + 3√3 ft + 6 ft
Total length of wood ≈ 14.2 ft (when rounded to one decimal place)
Therefore, the approximate length of wood needed to trim the window is approximately 14.2 ft.
Tobias wants to add a wooden trim to a triangular window with the dimensions shown.
The diagram shows a right-angled triangle. The angle of the top vertex is 60 degrees, and the angle of the left vertex is 30 degrees. The length of the hypotenuse is 6 ft.
What is the approximate length of wood needed to trim the window?
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