Answer:
The distance to the horizon, from the climber’s viewpoint to the nearest tenth is, 151.6 mi
Step-by-step explanation:
Using Pythagoras theorem:
[tex]\text{Hypotenuse side}^2 = \text{Adjacent side}^2 + \text{Opposite side}^2[/tex]
We know that:
Radius of the earth ≈ 3959 mi.
The radius of a circle meets a tangent at 90 degree.
As per the statement:
A mountain climber is at an altitude of 2.9 mi above the earth’s surface.
See the diagram as shown below in the attachment:
In triangle ABO
Hypotenuse side = AO = 3959 +2.9 = 3961.9 mi
Opposite side = AB = x mi and
Adjacent side = 3959 mi
Substitute these we have;
[tex]3961.9^2 = 3959^2+x^2[/tex]
⇒[tex]15696651.6 = 15673681 +x^2[/tex]
⇒[tex]22970.5 = x^2[/tex]
⇒[tex]\sqrt{22970.5} = x[/tex]
Simplify:
151.560219 mi = x
or
x =151.60219 mi
therefore, the distance to the horizon, from the climber’s viewpoint to the nearest tenth is, 151.6 mi
