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

i suppose it should be (y=2x-5)

step-by-step explanation:

the answer is:

the lateral area is equal to

to find the lateral area of the square pyramid, first we need to find the perimeter of the base, and then, find the lateral area using the following formulas:

where,

s, is the base length

slant height, is the height of a the side of the pyramid

we are given:

now, calculating the perimeter of the base, we have:

then, calculating the lateral area:

hence, we have that the lateral area is equal to

have a nice day!