Question

trig word problems solve for angle
score: 2/3 penalty: none
question
bashir leans a 16 - foot ladder against a wall. if the ladder reaches 14.3 feet up the wall, what angle does it form with the ground? round your answer to the nearest tenth of a degree.

Explanation:

Step1: Identify the trig - function

The ladder against the wall forms a right - triangle, where the length of the ladder is the hypotenuse ($c = 16$ feet) and the height on the wall is the opposite side ($a=14.3$ feet) to the angle we want to find. We use the sine function $\sin\theta=\frac{a}{c}$.

Step2: Calculate the sine value

Substitute $a = 14.3$ and $c = 16$ into the sine formula: $\sin\theta=\frac{14.3}{16}=0.89375$.

Step3: Find the angle

To find the angle $\theta$, we take the inverse sine (arcsine) of 0.89375. So, $\theta=\sin^{- 1}(0.89375)$. Using a calculator, $\theta\approx63.3^{\circ}$.

Answer:

$63.3^{\circ}$