Question

1. a driveway rises 2.2 m from the street level to the carport, which is a horizontal distance of 5.8 m from the street. a) how long is the driveway? b) what is its angle of elevation?

Explanation:

Step1: Apply Pythagorean theorem for length

Let the vertical rise be $a = 2.2$ m and the horizontal distance be $b=5.8$ m. The length $l$ of the driveway (hypotenuse of a right - triangle) is given by $l=\sqrt{a^{2}+b^{2}}$.
$l=\sqrt{(2.2)^{2}+(5.8)^{2}}=\sqrt{4.84 + 33.64}=\sqrt{38.48}\approx6.2$ m

Step2: Use tangent function for angle of elevation

Let the angle of elevation be $\theta$. We know that $\tan\theta=\frac{a}{b}$, where $a = 2.2$ m and $b = 5.8$ m.
$\theta=\arctan(\frac{2.2}{5.8})\approx\arctan(0.3793)\approx20.7^{\circ}$

Answer:

a) Approximately $6.2$ m
b) Approximately $20.7^{\circ}$