Question

question bentley leans a 22 - foot ladder against a wall so that it forms an angle of 74° with the ground. how high up the wall does the ladder reach? round your answer to the nearest hundredth of a foot if necessary. answer attempt 1 out of 2 feet submit answer show examples

Explanation:

Step1: Identify the trigonometric relationship

We know that the ladder forms a right - triangle with the wall and the ground. The length of the ladder is the hypotenuse ($c = 22$ feet), and we want to find the height ($a$) up the wall. The angle with the ground is $\theta=74^{\circ}$. We use the sine function: $\sin\theta=\frac{a}{c}$.

Step2: Substitute the values into the formula

Since $\sin\theta=\frac{a}{c}$, and $c = 22$, $\theta = 74^{\circ}$, we have $a=c\times\sin\theta$.
Substitute $c = 22$ and $\sin(74^{\circ})\approx0.9613$ into the formula: $a = 22\times0.9613$.

Step3: Calculate the value

$a=22\times0.9613 = 21.1486$.

Answer:

$21.15$