Question

a 20 - foot ladder is set up against a building so that the ladder makes an angle of 73° with the ground. the height, h, is the vertical distance from the top of the ladder to the base of the building. the base, b, is the horizontal distance from the bottom of the ladder to the base of the building. what is the approximate height - to - base ratio?
sin 73^{circ}approx0.9563
cos 73^{circ}approx0.2924
\tan 73^{circ}approx3.2709

Explanation:

Step1: Recall trigonometric - ratio relation

In a right - triangle formed by the ladder, the building, and the ground, $\tan\theta=\frac{h}{b}$, where $\theta = 73^{\circ}$, $h$ is the height and $b$ is the base.

Step2: Substitute the angle value

Given that $\tan73^{\circ}\approx3.2709$, and $\frac{h}{b}=\tan73^{\circ}$. So the height - to - base ratio $\frac{h}{b}\approx3.27:1$.

Answer:

C. $3.27:1$