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# What is the distance to the earth’s horizon from point P?

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What is the distance to the earth’s horizon from point P?

Round to the nearest tenth.

A skydiver is at an altitude of 1.4 mi above the earth’s surface.

From the skydiver’s viewpoint, what is the distance to the horizon?

Round to the nearest tenth.

Guest May 7, 2017
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[Distance to the Horizon]^2 =Height of the skydiver x Diameter of the Earth

D^2 = 1.4 x 7918

D^2 = 11,085.2

D = Sqrt(11,085.2)

D = ~ 105.28628......miles - Distance to Horizon.

Guest May 7, 2017
edited by Guest  May 7, 2017
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The  side of the triangle with a length of 3959 + 1.4   is the hypotenuse of a right triangle with the Earth's radius forming another leg.....the distance from the skydiver to the horizon, "x" is given by :

sqrt[ (3969 + 1.4)^2  - 3969^2 ]  ≈ 105.296 miles

CPhill  May 8, 2017
edited by CPhill  May 8, 2017
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What is the distance to the earth’s horizon

Tangent Secant Theorem

What is the distance to the earth’s horizon from point P?

Round to the nearest tenth.

r = 3959 mi

$$x^2 = 15.6 \cdot (15.6 + 2\cdot 3959) \\ x = 351.8\ \text{mi}$$

A skydiver is at an altitude of 1.4 mi above the earth’s surface.

From the skydiver’s viewpoint, what is the distance to the horizon?

Round to the nearest tenth.

r = 3959 mi

$$x^2 = 1.4\cdot (1.4 + 2\cdot 3959) \\ x = 105.3\ \text{mi}$$

heureka  May 8, 2017