# if a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.

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## Question 8 If a man standing on a platform 3m above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.

Question 8 If a man standing on a platform 3m above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.

Byju's Answer Standard X Mathematics

Angle of Elevation and Angle of Depression

Question 8 If... Question

**Question 8**

If a man standing on a platform 3m above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.

Open in App Solution

The statement is false.

We know that, if P is a point above the lake at a distance "d", then the reflection of the point in the lake would be at the same distance "d". Also, the angle of elevation and depression from the surface of the lake is same.

Here, the man is standing on a platform 3m above the surface, so its angle of elevation to the cloud and angle of depression to the reflection of the cloud is not same.

Another method- From the figure- Let, P M = y C M = O C = h tan θ 1 = h − 3 y ⇒ y = x − 3 tan θ 1 . . . ( i ) And, tan θ 2 = x + 3 y ⇒ y = x + 3 tan θ 2 . . . . ( i i ) From (i) and (ii) x − 3 tan θ 1 = x + 3 tan θ 2 ⇒ tan θ 1 = x − 3 x + 3 tan θ 2 ∵ x − 3 x + 3 = 1 ⇒ x − 3 = x + 3

Which is not possible.

**Hence, given statement is fales.**

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EXEMP - Grade 10 - Mathematics - Introduction to Trigonometry and its Applications - Q23

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SIMILAR QUESTIONS

**Q.**State true or false:If a man standing on a platform 3 meters above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.

**Q.**

If a man standing on a platform 3m above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection. Say whether the given statement is true or false.

**Q.**

If the angle of elevation of a cloud from a point 60 m above a lake is 30 and the angle of depression of its reflection in the lake be 60 .find the height of the cloud from the surface of the lake.

**Q.**The angle of elevation of a cloud from a point

h

meters above the surface of a lake is

300

and the angle of depression of its reflection is

600

. Then the height of the cloud above the surface of the lake is

**Q.**The angle of elevation of a cloud from a point

h

meters above the surface of a lake is

30 o

and the angle of depression of its reflection is

60 o

. Then the height of the cloud above the surface of the lake is

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Angle of Elevation and Angle of Depression

Standard X Mathematics

## If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the

If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of it

## If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection. Write ‘True’ or ‘False’ and justify your answer

**Solution:**

Given, a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake.

We have to determine if the angle of elevation of the cloud is equal to the angle of depression of its reflection.

Let M be the position where a man is standing on a platform.

C is the cloud

MO is the height of the platform from the surface of the lake.

MO = 3 m

Let θ₁ be the angle of elevation

Let θ₂ be the angle of depression

Height of reflection of the cloud = (h + 3) m

In triangle MPC, tan θ₁ = CM/PM tan θ₁ = h/PM

PM = h/tan θ₁ ------------------- (1)

In triangle MPC’, tan θ₂ = C’M/PM tan θ₂ = (h + 3)/PM

PM = (h + 3)/tan θ₂ ----------------- (2)

From (1) and (2),

h/tanθ₁ = (h + 3)/tanθ₂

h(tanθ₂) = (h + 3) tanθ₁

So, tanθ₁ = h/(h + 3) tanθ₂

It is clear that θ₁ ≠ θ₂

Therefore, the angle of elevation is not equal to the angle of depression.

**✦ Try This:**From the top of a cliff 200ft. high, the angle of depression of the top and bottom of the tower are observed to be 30 and 60 respectively. The height of the tower is

**☛ Also Check:**NCERT Solutions for Class 10 Maths Chapter 8

**NCERT Exemplar Class 10 Maths Exercise 8.2 Problem 8**

## If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection. Write ‘True’ or ‘False’ and justify your answer

**Summary:**

The statement “If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection” is false

**☛ Related Questions:**

The value of 2sinθ can be a+(1/a), where a is a positive number and a≠1. Write ‘True’ or ‘False’ an . . . .

cos θ = (a2+b2)/2ab, where a and b are two distinct numbers such that ab > 0. Write ‘True’ or ‘False . . . .

The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the . . . .

## State true or false if a man standing on a platform $3\\;{\\text{m}}$above from the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.\n \n \n \n \n

State true or false if a man standing on a platform $3\\;{\\text{m}}$above from the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.\n ...

State true or false if a man standing on a platform3m 3m

above from the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.

Last updated date: 14th Mar 2023

• Total views: 268.2k • Views today: 6.48k Answer Verified 268.2k+ views

**Hint:**In this question use the concept of the tangent that is, it is the ratio of the length of the perpendicular to the length of the base. Then compare the tangent of angle

θ 1 θ1 and θ 2 θ2

to find whether the given statement is true or false.

**Complete step-by-step answer:**

As per the given statement, let us assume a man standing on a platform at a point A and let C be the point above the surface of a lake observes a cloud.

Let us, consider the following diagram which shows two triangles that is triangle

BAD BAD and triangle CAB CAB ,

Let the height of the cloud from the surface of the platform is

h h

and the angle of elevation of the cloud is

θ 1 θ1 .

Now, at the same point the man observes cloud reflection in the lake at this the height is

h+3 h+3

because in the lake the platform height is also added.

In triangle BAD BAD , tan θ 1 = BD AB tan θ 1 = h AB tan θ 1 h = 1 AB ⋅⋅⋅⋅⋅⋅(1)

tanθ1=BDABtanθ1=hABtanθ1h=1AB⋅⋅⋅⋅⋅⋅(1)

In triangle CAB CAB , tan θ 2 = CB AB tan θ 2 = h+3 AB tan θ 2 h+3 = 1 AB ⋅⋅⋅⋅⋅⋅(2)

tanθ2=CBABtanθ2=h+3ABtanθ2h+3=1AB⋅⋅⋅⋅⋅⋅(2)

Now, on comparing above equations,

tan θ 1 h = tan θ 2 h+3 tan θ 2 =( h+3 h )tan θ 1

tanθ1h=tanθ2h+3tanθ2=(h+3h)tanθ1

Therefore, θ 1 ≠ θ 2 θ1≠θ2

. Hence, if a man standing on a platform

3m 3m

above from the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is not equal to the angle of depression of its reflection. Thus, the given statement is false.

**Note:**We know that calculus and algebra are based on trigonometry. It is widely used in creation of maps and to calculate heights. It is also used in many fields such as architecture, to make designs. In physics and mathematics, it is used to find the components of vectors

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