Answer:
Approximately 460 ft
Step-by-step explanation:
In any question where we have:
- A right triangle
- An given angle, and
- A given side
And we're asked to find:
We're gonna be using some trigonometry. The first question we've gotta ask is what we're looking for, and how the angles and sides relate to that. We're given:
- The angle of elevation, 49°
- The distance to the base, 400 ft
And we're looking for:
- The height of the hill, which I'll call h.
How do our sides relate to the angle? Well, the 400 ft side is adjacent to 49°, and the side h is opposite. From SOH-CAH-TOA, we can see that the last trig function, tangent, is equal to opposite/adjacent. Let's turn this into an equation to bring it all together:
[tex]\tan{49^\circ}=h/400[/tex]
Solving for h, we find that
[tex]h=400\tan{49^\circ}\approx400(1.15)=460[/tex]
So the heigh of the hill is approximately 460 ft.
