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

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is

could you provide figure.