If the altitude of an equilateral triangle is 10, what is the length of each side?

All the angles of an equilateral triangle measures 60 degrees. The altitude measuring 10 is a side of the right triangle opposite to the angle. The side of the equilateral triangle becomes the hypotenuse to the right triangle generated by drawing the altitude. To get the measure of the hypotenuse, multiply the altitude to the sine of 60 degrees. The operation gives an answer of 8.66. 

Thus, the length of each side of the equilateral triangle measures approximately 8.66 units. 

Height of shuttle at that instant  = 1.17 miles

Step-by-step explanation:

Refer the given figure.

C is the position of rocket and B is the position of observer.

Here we need to find AC, that is the height of shuttle at that instant.

Using trigonometric rules on ΔABC, we have

     

Height of shuttle at that instant = AC = 1.17 miles