Question

A skydiver s jumps from a plane at an altitude of 3km the radius of the earth is approximately 6400km how far is the horizon h from the skydiver when she leaves the plane calculate this distance to the nearest kilometer​

Answer 1

196 km

Explanation:

See attached figure

The skydiver is at a height of 3 km above the earth surface at point S

Point H represents the horizon as seen by the skydiver

CH represents the radius of the earth = 6400

SH is the line of sight from S to H and is tangential to the circle representing the earth's surface

Sine SH is tangent to the circle, CH is perpendicular to SH

Therefore the triangle CSH is a right triangle with m∠H = 90°

The hypotenuse of the triangle is CS = 6400 + 3 = 6403 km

The legs are CH = 6400 and SH which is to be determined

Using the Pythagorean theorem

CS² = CH² + SH²

Plugging in knowns:
6403² = 6400² + SH²

SH² = 6403² - 6400² = 38409

SH = √(38409) ≈ 195.98 km ≈ 196 km rounded to nearest km