You can use your knowledge of triangles to choose the correct answer as
24 ft
because you know that the ladder must be longer than 23 ft and will be very near 23 ft in length.
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Using trigonometry, we know the ratio of the side opposite to the hypotenuse for an angle in a right triangle is the sine of that angle. (The SOH of SOH CAH TOA.)
Sin(angle) = Opposite/Hypotenuse
sin(75°) = (height up the wall)/(ladder length)
sin(75°) = (23 ft)/(ladder length)
Multiplying this equation by (ladder length) and dividing by sin(75°), we get
(ladder length) = (23 ft)/sin(75°) ≈ 23.811 ft ≈ 24 ft
