Answer:
33.7°
Step-by-step explanation:
To find the approximate angle formed by the horizontal and the roof, we can use basic trigonometry.
Given:
- Opposite: 4 feet
- Adjacent: 6 feet
Using the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right triangle, we have:
[tex] \tan(\theta) = \dfrac{\textsf{Opposite}}{\textsf{Adjacent}} [/tex]
[tex] \tan(\theta) = \dfrac{4}{6} [/tex]
[tex] \tan(\theta) = \dfrac{2}{3} [/tex]
Now, we can find the angle [tex] \theta [/tex] by taking the inverse tangent of this ratio:
[tex] \theta = \tan^{-1} \left(\dfrac{2}{3}\right) [/tex]
Using a calculator, we can find the approximate value of [tex] \theta [/tex].
[tex] \theta \approx 33.690067525979 [/tex]
[tex] \theta \approx 33.7 \textsf{ feet (in nearest tenth)}[/tex]
So, the approximate angle formed by the horizontal and the roof is [tex] \approx 33.7^\circ [/tex].
