Question

1. a 5 - m - long ladder is leaning up against the side of a barn. it reaches 4.2 m up the side of the barn wall. find the angle the ladder makes with the ground.

Explanation:

Step1: Identify the trig - function

We know the length of the ladder (hypotenuse $c = 5$ m) and the height it reaches on the wall (opposite side $a=4.2$ m) with respect to the angle between the ladder and the ground. We use the sine function $\sin\theta=\frac{a}{c}$.
$\sin\theta=\frac{4.2}{5}$

Step2: Calculate the angle

$\theta=\sin^{- 1}(\frac{4.2}{5})$.
$\theta=\sin^{-1}(0.84)$
Using a calculator, $\theta\approx57.1^{\circ}$

Answer:

The angle the ladder makes with the ground is approximately $57.1^{\circ}$