Height and Distance
- The ratio of the length of a rod and its shadow is 1: √3 .The angle of elevation of the sun is :
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Let us draw the figure from the given question.
Let, AB be the rod and AC be its shadow.
Let us assume the angle of elevation ∠ACB = θ.
Correct Option: A
Let us draw the figure from the given question.
Let, AB be the rod and AC be its shadow.
Let us assume the angle of elevation ∠ACB = θ.
According to given question,
AB : AC = 1 : √3
we know that ,In triangle ACB , tanθ = AB AC ∴ tanθ = 1 √3
⇒ tanθ = tan30°
⇒ θ = 30°
Hence ,The angle of elevation of the sum is 30° .
- On the ground level the angle of elevation of the top of a tower is 30°, On moving 20 m nearer the tower, the angle of elevation found to be 60°. The height of the tower is ?
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Let us draw a figure below from the given question.
Let AB = h meter be the height of the towers. B and C are two points such that BC = 20 m; ∠ADB = 30° and ∠ACB = 60° BC = x meter (let us assume)
Correct Option: B
Let us draw a figure below from the given question.
Let AB = h meter be the height of the towers. B and C are two points such that BC = 20 m; ∠ADB = 30° and ∠ACB = 60° BC = x meter (let us assume)
Now, from right triangle ABC,
x = h cot 60°
⇒ x = h/√3 meter
Again, from right triangle ABD,
h = (20 + x) tan 30°
put the value of x in above equation.
∵ x = h/√3
⇒ h = (20 + h/√3) x 1/√3 ( ∵ tan 30° = 1/√3 )
⇒ h - h/3 = 20/√3 ⇒ 2h/3 = 20/√3
∴ h = 20 x 3/2√3 = 10√3 m
- The angle of elevation of the top of two vertical towers as seen from the middle point of the line joining the foot of the towers are 60° and 30° respectively. The ratio of the heights of the towers is ?
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Let us draw a figure below as per given question.
Let AB and CD be two towers of height h1 and h2 respectively and O the mid-point of the line joining the foots A and C of the towers.
Correct Option: D
Let AB and CD be two towers of height h1 and h2 respectively and O the mid-point of the line joining the foots A and C of the towers.
Let OA = OC = x
Then h1 = x tan 60° = x√3
and h2 = x tan 30° = x/√3
∴ h1 /h2= 3/1.
Hence, h1 : h2 = 3 : 1
- A person standing on the bank of river finds that the angle of elevation of the top of a tower on opposite side bank is 45°. Which of the following statement is correct
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Let us draw a figure below as per given question.
Let AB = h m be the height of the tower, BC = x m be the breadth of the river and also ∠ACB = 45°
Correct Option: B
Let us draw a figure below as per given question.
Let AB = h m be the height of the tower, BC = x m be the breadth of the river and also ∠ACB = 45°
Now from right triangle ABC
tan 45° = h/x ⇒ 1 = h/x
∴ x = h
Hence, breadth of the river = height of the tower
- A vertical pole is 75m high. Find the angle subtended by the pole a point 75 m away from its base.
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Let us draw a figure below as per given question.
Let AB = 75 m be the height of pole and C is a point on the ground such that BC = 75m
Correct Option: B
Let us draw a figure below as per given question.
Let AB = 75 m be the height of pole and C is a point on the ground such that BC = 75m
Now, from right triangle ABC.
tan ∝ = AB/BC = 75/75
⇒ tan∝ = 1
∴ ∝ = 45°
