Applications of Trigonometry

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Applications of Trigonometry

1.A tower stands vertically on the ground. From a point which is 15 meter away from the foot of the tower, the angle of elevation of the top of the tower is 450. What is the height of the tower”?
Solution :

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Let the height of the tower = h m

Distance of the point of observation from the foot of the tower =15 cm.

Angle of elevation of the top of the tower = 45°

From the figure tan θ =

opp. side adj. side

tan 45° =⇒ 1 =

h15

∴ h = 1 × 15 = 15 m

Question 2:
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground by making 300 angle with the ground. The distance between the foot of the tree and the top of the tree on the ground is 6m. Find the height of the tree before falling down.
Solution :

Distance between the foot of tree and the point of contact of the top of the tree on the ground = 6 cm.
Let the length of the remaining part be = h m.
Let the length of the broken part be = x m.
Angle made by the broken part with the ground = 30°.
From the figure
tan 30° =
∴ h = 63√=3×23√ = 2√3 m
Also cos 30° =
⇒ x = 6×23√ 4√3
∴ Height of the tree = broken part + remaining part
= x + h
= 2√3 + 4√3 = 6√3 m
= 6 × 1.732
≃ 10.392m

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Question 3:
A contractor wants to set up a slide for the children to play in the park. He wants to set it up at the height of 2 m and by making an angle of 300 with the ground. What should be the length of the slide?

Height of slide = 2 m

Let the length of the slide = x m.
Angle made by the slide with the ground = 30°
From the figure
sin 30° = 2x
⇒ 12 = 2x
⇒ x = 2 × 2 = 4 m
Length of the slide = 4 m.

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Question 4:
Length of the shadow of a 15 meter high pole is 5 $\sqrt{3}$ meters at 7 0’clock in the morning. Then, what is the angle of elevation of the Sun rays with the ground at the time?
Solution :

Height of the pole = 15 m
Length of the shadow = 5√3 m
Let the angle of elevation be ‘θ’.
Then from the figure
tan θ = 1553√=5×3√×3√5×3√ = √3
tan θ = √3 = tan 60°
∴ θ = 60°
∴ Angle of elevation of Sun rays with the ground = 60°.

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Question 5:
You want to erect a pole of height 10 m with the support of three ropes. Each rope has to make an angle 300 with the pole. What should be the length of the rope?
Solution :

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Question 6:
Suppose you are shooting an arrow from the top of a building at an height of 6 m to a target on the ground at an angle of depression of 600. What is the distance between you and the object?

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Question 7:
An electrician wants to repair an electric connection on a pole of height 9 m. He needs to reach 1. 8 m below the top of the pole to do repair work. What should be the length of the ladder which he should use, when he climbs it at an angle of 600 with the ground? What will be the distance between foot of the ladder and foot of the pole?
Solution :

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Question 8:
A boat has to cross a river. It crosses the river by making an angle of 600 with the bank of the river due to the stream of the river and travels a distance of 600m to reach the another side of the river. What is the width of the river’?

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Question 9:
An observer of height 1.8 m is 13.2 m away from a palm tree. The angle of elevation of the top of the tree from his eyes is 450. What is the height of the palm tree?