Dustin is standing at the edge of a vertical cliff, 40 meters high, which overlooks a clear lake. he spots a fluffy white cloud above the lake, which from his point of view has an angle of elevation of $30^\circ.$ he also sees the reflection of the cloud in the lake, which has an angle of depression of $60^\circ.$ find the height of the cloud above the lake, in meters.

53.33 meters

Step-by-step explanation:

Let AB represents the height of the cliff,

( where, A is top and B is bottom ),

Also, C and D represents the shadow of the cloud and cloud in the sky respectively,

Suppose E is a point in the segment CD,

Such that,

AB = DE = 40 meters,

According to the question,

Since,

Now,

Hence,

The height of the cloud above the lake = CE + ED

1e+27

step-by-step explanation: