Question

An A-frame cabin is 26.23 feet high at the center and the angle the floor makes with the base is 53. How

wide is the base?

Answer 1

To find the width of the base of the A-frame cabin, we can use trigonometry. Let x represent the width of the base. We can set up the equation tan(53) = 26.23 / x and solve for x. The width of the base is approximately 22.61 feet.

Step-by-step explanation:

To find the width of the base of the A-frame cabin, we can use trigonometry. We can use the tangent function to relate the height of the cabin, the angle the floor makes with the base, and the width of the base. Tangent is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, the height of the cabin is the opposite side and the width of the base is the adjacent side.

Let x represent the width of the base. We can set up the equation tan(53) = 26.23 / x. We can solve for x by multiplying both sides of the equation by x and then dividing both sides by tan(53). The resulting equation is x = 26.23 / tan(53). Using a calculator, we can find that x is approximately 22.61 feet.

Answer 2

60.84 feet

solution,

`tan \: theta = (perpendicular)/(base) \\ tan \: (53) = (bc)/(ac) \\ tan \: (53) = (26.23)/(ac) \\ ac = (26.23)/(0.4311) \\ ac = 60.84 \: feet`

Hope this helps...

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