Answer:
[tex]\theta \approx 82.34^\circ[/tex]
Step-by-step explanation:
Please refer to the attached diagram. (Apologies if the shading or resolution is a bit off.)
So, we want to find θ.
Since we formed a right triangle, we can use right triangle ratios.
We know the measure of the adjacent side to θ and the hypotenuse.
Therefore, we will use the cosine ratio:
[tex]\displaystyle \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}[/tex]
The adjacent side is 2 and the hypotenuse is 15. By substitution:
[tex]\displaystyle \cos(\theta)=\frac{2}{15}[/tex]
Now, we will take the inverse cosine of both sides. So:
[tex]\displaystyle \theta=\cos^{-1}\Big(\frac{2}{15}\Big)[/tex]
Use a calculator. Hence:
[tex]\theta \approx 82.34^\circ[/tex]
The angle between the ground and the ladder is about 82.34°.
