Laser beem directed toward the moon?

[Timcago]

The Moon has a radius of approximately 1000 miles and is approximately 240000 miles from Earth. A laser beam is directed toward the center of the Moon and fired. The beam strays 0.5 degrees from its intended target. How far away from the target is the beam when it reaches the Moon? Will it hit the Moon?

 

[pka]

Here is a hint.
The answer depends upon tan(0.5deg).

 

[galactus]

Here's a diagram. Try to find x.

 

[Timcago]

Like this?

--------------->x
Tan(.5)= ------------
----------->240000

240000*tan(.5) = 131112.6

The Laser is 131112.6 miles from the target when it reaches the moon. It will not hit.

 

[pka]

You have your calculation device set to RADIAN MODE.
You need to change to DEGREE MODE.
Then you will get 2094.448.

 

[galactus]

No, you have your calculator set on radians. It asked for degrees.

You could also leave it in radians and enter \(\displaystyle 240000tan(\frac{\pi}{360})\)

 

[Timcago]

Good eye. Thankyou