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If the length of the shadow of a tower is √3 times that of its height, then the angle of elevation of the sun is
- a)30°
- b)45°
- c)60°
- d)75°
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If the length of the shadow of a tower is √3 times that of its h...
Let AB be the tree and AP be the shadow.
Let AB = x meters. Then AP = x√3 meters
Also ∠APB = θ
In right angled triangle ABP
Let AB = x meters. Then AP = x√3 meters
Also ∠APB = θ
In right angled triangle ABP
Therfore the angle of elevation of the Sun is 30°.
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If the length of the shadow of a tower is √3 times that of its h...
If the length of the shadow of a tower is 20 meters and the angle of elevation from the tip of the shadow to the top of the tower is 40 degrees, we can use trigonometry to find the height of the tower.
Let's assume that the height of the tower is h meters.
In a right triangle formed by the tower, its shadow, and the line connecting the top of the tower to the tip of the shadow, the angle of elevation is 40 degrees.
Using the trigonometric function tangent (tan), we can write:
tan(40 degrees) = h / 20
Rearranging the equation to solve for h, we have:
h = 20 * tan(40 degrees)
Using a calculator, we find:
h ≈ 20 * 0.839 = 16.78 meters
Therefore, the height of the tower is approximately 16.78 meters.
Let's assume that the height of the tower is h meters.
In a right triangle formed by the tower, its shadow, and the line connecting the top of the tower to the tip of the shadow, the angle of elevation is 40 degrees.
Using the trigonometric function tangent (tan), we can write:
tan(40 degrees) = h / 20
Rearranging the equation to solve for h, we have:
h = 20 * tan(40 degrees)
Using a calculator, we find:
h ≈ 20 * 0.839 = 16.78 meters
Therefore, the height of the tower is approximately 16.78 meters.
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