Chapter 10.8, Problem 15PSB

To determine

To Find: To find distance HE

Answer to Problem 15PSB

  $900$

Explanation of Solution

Given Information:$\begin{array}{l}\text{1)}\text{Diameter of the earth = 8000 mi}\text{.}\\ \text{2)}\text{Distance of Heavenly Helen from erth surface = 100 mi}\end{array}$

Formula Used:The tangent at a point on a circle is at right angles to this radius.

Calculation:

  

  $\begin{array}{l}\text{Let O be the center of the circle}\text{. And S be the point on surface of}\\ \text{earth at which line OH intersect}\text{.}\\ \text{By the theorem,angle OEH}=90°\text{.}\\ \text{Using Pythagoras theorem,}\\ O{H}^2=O{E}^2+E{H}^2\mathrm{.......}(1)\\ OH=OS+SH\\ OH=4000+100\\ OH=4100\\ \text{Now, putting the value in eq}\text{. 1 we get}\text{.}\\ {4100}^2={4000}^2+E{H}^2\\ E{H}^2={4100}^2-{4000}^2\\ E{H}^2=(4100-4000)\cdot (4100+4000)\\ E{H}^2=100\cdot 8100\\ E{H}^2=810000\\ EH=\sqrt{810000}\\ EH=900\end{array}$