Question

1. tyler is helping his mother paint the eavestrough on their house. he leans the ladder on the bricks 4 m above the ground. the bottom of the ladder is 2 m away from the house. a) safety guidelines state that the maximum slope of a ladder should be 4.000. what is the angle of elevation of a ladder placed at this slope? round your answer to the nearest degree. b) does tyler have the ladder positioned safely?

Explanation:

Step1: Recall slope - angle relationship

The slope $m$ of a line is related to the angle of elevation $\theta$ by $m = \tan\theta$.

Step2: Solve for the angle when $m = 4$

Given $m = 4$, we have $\tan\theta=4$. Then $\theta=\arctan(4)$. Using a calculator, $\theta=\arctan(4)\approx76^{\circ}$ (rounded to the nearest degree).

Step3: Calculate the slope of Tyler's ladder

The height of the ladder on the wall $y = 4$ m and the distance of the bottom of the ladder from the house $x = 2$ m. The slope of Tyler's ladder $m_{Tyler}=\frac{y}{x}=\frac{4}{2}=2$.

Step4: Determine safety

Since the maximum safe slope is $m = 4$ and $m_{Tyler}=2<4$, Tyler has the ladder positioned safely.

Answer:

a) $76^{\circ}$
b) Yes