Answer:
θ = 17.45°
Step-by-step explanation:
Given that,
Length of a ladder = 40 foot
Height of a building = 12 feet
We need to find the angle of elevation that the ladder makes with the ground.
40 foot will be the hypotenuse and 12 feet will be the perpendicular distance.
Using trigonometry for this:
[tex]\sin\theta=\dfrac{P}{H}\\\\\sin\theta=\dfrac{12}{40}\\\\\theta=17.457^{\circ}[/tex]
So, the angle of elevation that the ladder makes with the ground is 17.45°.
The angle of elevation is [tex]17^\circ[/tex] to the nearest degree
The right-angled triangle formed can be solved for the angle of elevation if we note that
So, the trigonometric ratio to be used here is the [tex]sin\theta[/tex]. That is
[tex]sin\theta=\dfrac{\text{height of the building}}{\text{length of ladder}}[/tex]
substituting the values
[tex]sin\theta=\dfrac{12}{40}\\=\dfrac{3}{10}[/tex]
Now, to find the angle of elevation, [tex]\theta[/tex]
[tex]\theta=sin^{-1} \left(\dfrac{3}{10} \right)\\\approx 17^\circ \text{ (to the nearest degree)}[/tex]
Learn more trigonometry here: https://brainly.com/question/1980819
