Question

1. -/1 points 0/2 submissions used a 22 - foot - tall ladder leans against a building so that the angle between the ground and the ladder is 67°. how high (in ft) does the ladder reach on the building? (round your answer to the nearest foot.)

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle situation where the length of the ladder is the hypotenuse ($c = 22$ ft) and we want to find the height ($a$) the ladder reaches on the building. The angle between the ladder and the ground is $\theta=67^{\circ}$. We use the sine function since $\sin\theta=\frac{a}{c}$.

Step2: Solve for the height

We know that $a = c\times\sin\theta$. Substituting $c = 22$ and $\theta = 67^{\circ}$, and $\sin(67^{\circ})\approx0.9205$. So $a=22\times0.9205 = 20.251$.

Step3: Round the answer

Rounding $20.251$ to the nearest foot gives $20$ ft.

Answer:

$20$ ft