Question

A climber is standing at the top of mount kazbek, approximately 3.1 miles above sea level. the radius of the earth is 3959 miles. what is the climber's distance to the horizon? enter your answer as a decimal in the box. round only your final answer to the nearest tenth. mi

Answer 1

156.7

Explanation:

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Answer 2

In the figure below, the radius, AB=AD=3959 mi, the climber is at position C. BC=3.1 mi. CD=x mi, is the distance from the climber to the horizon. Thus to solve for x we proceed as follows:
AC=3959+3.1=3962.1 mi
To evaluate for x we use the Pythagorean theorem, this is given by:
c^2=a^2+b^2
c=AC is the hypotenuse
a and b are the legs
plugging in the values we shall have:
3962.1^2=x^2+3959^2
x^2=3961.1^2-3959^2
x^2=24555.41
hence
x=156.7 mi

Answer: 156.7 mi