if the angle of elevation of a tower from a distance of 100m from its foot is 60*, then the height of tower is
height/100 = tan 60°
height = ..... ?
20
Let the height of tower be AB=100m. The length of the shadow caste is 10√3m.
Therefore, angle of elevation of sun =?
Let the angle be Φ.
Therefore tanΦ= AB/BC
AB/BC=30/10√3
Therefore,
Tan Φ= 3/√3*√3/√3
Therefore tan Φ=√3
And we know that tan√3=60°.
Hence sun's elevation is 60°.
To find the height of the tower, we can use trigonometry. Let's draw a diagram to help visualize the problem.
/|
/ |
/ |h
/ |
/θ |
/_____|
100m
In the diagram, the tower is represented by a vertical line segment of height 'h'. The angle of elevation from the horizontal line is denoted by θ which is given as 60 degrees. The distance from the foot of the tower to the point where the angle is measured is 100 meters.
We can use the trigonometric function tangent (tan) to relate the angle of elevation to the height of the tower.
Tangent (tan) of an angle (θ) is equal to the opposite side (height 'h') divided by the adjacent side (distance '100m').
tan(θ) = h / 100
To find h (the height), we can rearrange the formula:
h = tan(θ) * 100
Now, let's substitute θ with 60 degrees:
h = tan(60) * 100
Using a scientific calculator, we find that tan(60) is approximately 1.732.
h = 1.732 * 100
Therefore, the height of the tower is approximately 173.2 meters.