Question

1. jake leaned a 12 - foot ladder against his house. if the angle formed by the ladder and the ground is 68°, how far from the base of the house did he place the ladder?

Explanation:

Step1: Identify the trig - ratio

We have a right - triangle where the length of the ladder is the hypotenuse ($c = 12$ feet) and we want to find the adjacent side ($x$) to the given angle $\theta=68^{\circ}$. We use the cosine function, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$.
$\cos\theta=\frac{x}{c}$

Step2: Substitute the values

Substitute $\theta = 68^{\circ}$ and $c = 12$ into the cosine formula.
$x = c\times\cos\theta$
$x=12\times\cos(68^{\circ})$

Step3: Calculate the value

We know that $\cos(68^{\circ})\approx0.3746$.
$x = 12\times0.3746$
$x\approx4.4952\approx4.5$ feet

Answer:

The ladder is placed approximately $4.5$ feet from the base of the house.