Question

shane is standing at the base of a truck - mounted stairway to board an aircraft. the elevation of the top of the stairway from the ground is 13 feet. the length of the stairway is 18 feet. what is the approximate angle made by the stairway with the ground? a. 35.84° b. 54.16° c. 43.76° d. 46.24°

Explanation:

Step1: Identify right - triangle elements

We have a right - triangle where the height (opposite side) is 13 feet and the hypotenuse is 18 feet. Let the angle between the stairway and the ground be $\theta$.

Step2: Use sine function

The sine of an angle in a right - triangle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. So, $\sin\theta=\frac{13}{18}$.

Step3: Find the angle

$\theta = \sin^{- 1}(\frac{13}{18})\approx46.24^{\circ}$

Answer:

D. $46.24^{\circ}$