a force of 24 lb is required to hold an 89 - lb crate on a hill. what angle does the hill make with the…

a force of 24 lb is required to hold an 89 - lb crate on a hill. what angle does the hill make with the horizontal?\nthe hill makes an angle of (square^{circ}) with the horizontal.\n(type your answer in degrees. round to the nearest integer as needed.)

a force of 24 lb is required to hold an 89 - lb crate on a hill. what angle does the hill make with the horizontal?\nthe hill makes an angle of (square^{circ}) with the horizontal.\n(type your answer in degrees. round to the nearest integer as needed.)

Answer

Explanation:

Step1: Resolve weight into components

The force required to hold the crate on the hill is equal to the component of the weight of the crate along the slope of the hill. Let the angle of the hill with the horizontal be $\theta$, the weight of the crate $W = 89$ lb and the force $F=24$ lb. The component of the weight along the slope is $W\sin\theta$. So we have $F = W\sin\theta$.

Step2: Solve for $\theta$

We can rewrite the equation $F = W\sin\theta$ as $\sin\theta=\frac{F}{W}$. Substituting $F = 24$ and $W = 89$, we get $\sin\theta=\frac{24}{89}$. Then $\theta=\sin^{- 1}(\frac{24}{89})$.

Step3: Calculate the value of $\theta$

Using a calculator, $\theta=\sin^{-1}(\frac{24}{89})\approx15.6^{\circ}$. Rounding to the nearest integer, $\theta\approx16^{\circ}$.

Answer:

$16$