**A contractor plans to install two slides for the children to play in a park for elder children. She wants to have a steep slide at a height of 6 m, and inclined at an angle of 60∘ to the ground. What should be the length of the slide (in m)?**

__Question:__**Options:**

A. | 3√3 m | |

B. | 5 m | |

C. | 4√3 m | |

D. | 6 m |

**Answer: Option C**

: C

The above figure represents the given situation.

In the given right-agled triangle,

sin(∠ACB)=ABAC⇒sin60∘=6AC⇒AC=6√32=12√3=4√3m∴lengthofslide=4√3m

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## More Questions on This Topic :

**A 1.8 m tall man is standing at some distance from a 31.8 m tall building. The angle of elevation from his eyes to the top of the building increases from 30∘ to 60∘ as he walks towards the building. Find the distance he walked towards the building.**

__Question 1.__- 30 m
- 20√3 m
- 20 m
- 30√3 m

**Answer: Option B**

: B

The situation can be represented by the figure above,

tan(∠ACB)=ABBC⇒tan60∘=30BC⇒BC=30tan60∘=10√3m⇒tan(∠ADB)=ABBD⇒tan30∘=30BD⇒BD=301√3=30√3m⇒Distancewalked=DC=BD−BC=30√3−10√3=20√3m

**A circus artist is climbing a 30 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. The height of the pole, if the angle made by the rope with the ground level is 30∘**

__Question 2._____

m.

:

The figure above represents the given situation.

In the given figure,

sin30∘=ABAC⇒AB=sin30∘×AC=AC2=302=15m.

**A circus artist is climbing a 30 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the distance of the pole to the peg in the ground, if the angle made by the rope with the ground level is 30∘.**

__Question 3.__- 5 m
- 15√3 m
- 18 m
- 20 m

**Answer: Option B**

: B

The figure above represents the given situation.

From the given firgure,

cos30∘=BCAC⇒BC=AC×cos30∘=30√32

=15√3m

**State whether the given statement is true or false:**

__Question 4.__The angle of depression is the angle between the line of sight of an observer below his horizontal line of sight.

- True
- False

**Answer: Option A**

: A

The angle of depression is the angle between the line of sight of anobserverbelow his horizontal line of sight.

**State whether the given statement is true or false:**

__Question 5.__The angle of elevation is the angle between the line of sight of an observer below his horizontal line of sight.

- True
- False

**Answer: Option B**

: B

The angle of elevation is the angle between the line of sight of an observer above his horizontal line of sight.

**A 1.8 m tall man is standing at some distance from a building. The angle of elevation from his eyes to the top of the building increases from 30∘ to 60∘ as he walks 20 m towards the building. Find the height of the building (in m).**

__Question 6.__- 10 m
- 20√3 m
- 20 m
- (10√3 + 1.8) m

**Answer: Option D**

: D

The situation can be represented by the figure above.

tan(∠ACB)=ABBC⇒BC=ABtan60∘.....(1)tan(∠ADB)=ABBD⇒tan30∘=ABBC+CD⇒BC+CD=ABtan30∘.....(2)on subtracting equation(1) from (2)⇒CD=ABtan30∘−ABtan60∘⇒AB=10√3

Hence, the height of the building is

= AB + BG = (10√3+1.8)m.

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