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### Course: Class 10 (Old)>Unit 9

Lesson 2: Two triangles problems

# Heights and distances word problem: height of a cloud above a lake

Let's solve a problem involving finding the height of a cloud given its angle of elevation and the angle of depression of its reflection. Created by Aanand Srinivas.

## Want to join the conversation?

• At , the creator says, "If there's a fish watching all this...", and since the fish is underwater, refraction will take place and the fish would see the object at higher than the height of the object placed. So should we ignore the refraction case or should we consider it with the general values of the refractive index of water and air, that's 1.33 and 1?
(1 vote)
• Yep!
In real world "refraction" took place when a you look at the fish inside the water ..
But As IN MATH of "class-10" we do not talk about refraction (Only in MATH)
It was consider as the given position is the perfect position of that object

Have a look at this :-

``__________________________________________                                            |         ___________                        |        | E A R T H |                       |                                            |                                            |           👨                                         /                                 |         /                                  |--------------------------- REFRACTION------|       /                                    |     /                                        /                                        🐟(Refraction Position)                                                                  🐟(Real Position)                                                                            ___________                         |       | W A T E R |                        |                                            |___________________________________________ |``

So what we can do to find real position ?
>>Applying refraction formulas and distance formula , some trig functions and then we get the real position .
Correct?

So what happens in math is they thereby give the real position to you and you have to calculate it easily
But as you move to the bigger classes "The Refraction" will came in roll with MATH
• what is the formula for finding angle of elevation and depression ?
• You can find any of the three trig ratios for any angle of the triangle, if any two of its three sides are given.
In most cases, you will find that the ratio which you found will be equal to any of the popular trig ratios.
For example, in a triangle with the lengths of the legs each equal to 1 cm, you can find the tangent of any angle (which, in this case, is 1) and you will find that it is equal to the tangent of 45 degrees.
So, you can conclude that the angle measures 45 degrees.
So, you can find any of the two non-90 angles of a right triangle.

Hope you understood :)