Question

calculator
anna has leaned a ladder against the side of her
house. the ladder forms a 72° angle with the
ground and rests against the house at a spot that is
6 meters high.
what length is the best approximation for the
distance along the ground from the bottom of the
ladder to the wall?
2 m
3 m
4 m
5 m

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(ABC\) (\(\angle B = 90^{\circ}\)), we know the opposite side (\(BC = 6\) m) and we want to find the adjacent side (\(AB\)) with respect to the angle \(\angle A=72^{\circ}\). The trigonometric ratio \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan A=\frac{BC}{AB}\).

Step2: Solve for \(AB\)

Since \(\tan A=\frac{BC}{AB}\), then \(AB = \frac{BC}{\tan A}\). Substitute \(BC = 6\) m and \(A = 72^{\circ}\). We know that \(\tan72^{\circ}\approx3.0777\). So, \(AB=\frac{6}{\tan72^{\circ}}\approx\frac{6}{3.0777}\approx2\) m.

Answer:

\(2\) m