A boy 1.5m tall,is 20m away from a tower 30m high.Determine the angle of elevation from his eye to the top of the tower.
Well, if the boy looks up at the tower, he might strain his neck. So, rather than calculating the angle of elevation, let's calculate the angle of inspiration! Now, the height of the tower is 30m, and the distance between the boy and the tower is 20m. So, the angle of inspiration can be calculated using the following equation:
Angle of Inspiration = arctan(opposite/adjacent)
Here, the opposite side is the height of the tower (30m) and the adjacent side is the distance between the boy and the tower (20m).
So, plugging it into the equation:
Angle of Inspiration = arctan(30/20)
Calculating the arctan(30/20), we get approximately 56.31 degrees.
Therefore, the angle of inspiration from the boy's eye to the top of the tower is approximately 56.31 degrees.
To determine the angle of elevation from the boy's eye to the top of the tower, we can use trigonometry.
The height of the tower can be considered as the opposite side (O) of a right triangle, while the horizontal distance from the boy to the tower can be considered as the adjacent side (A).
We have the following information:
Height of the tower (O) = 30m
Distance from the boy to the tower (A) = 20m
We can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side (tanθ = O/A), to find the angle of elevation (θ).
tanθ = O/A
Substituting the given values, we have:
tanθ = 30/20
Now let's calculate:
tanθ = 3/2
To find the angle θ, we can take the inverse tangent (also known as arctan or tan⁻¹) of both sides:
θ = tan⁻¹(3/2)
Using a calculator, we find:
θ ≈ 56.31 degrees
Therefore, the angle of elevation from the boy's eye to the top of the tower is approximately 56.31 degrees.
To determine the angle of elevation from the boy's eye to the top of the tower, we can use trigonometry, specifically the tangent function.
First, let's draw a diagram to understand the situation. The tower can be represented as a vertical line, and the boy can be represented as a point on the ground. The line connecting the boy's eye to the top of the tower would form a right triangle with the ground.
Now, we have the following information:
- The height of the tower = 30m
- The distance between the boy and the tower = 20m
- The boy's height = 1.5m
To find the angle of elevation, we need to find the ratio between the opposite side (tower height) and the adjacent side (distance between the boy and the tower). This ratio is defined as the tangent of the angle of elevation.
So, we can calculate the tangent of the angle as:
tan(angle) = opposite/adjacent
tan(angle) = height of the tower/distance between the boy and the tower
tan(angle) = 30m/20m
tan(angle) = 3/2
Now, to find the angle itself, we can take the inverse tangent (also called arctan or tan^-1) of both sides, which will give us the angle itself instead of the ratio:
angle = arctan(3/2) ≈ 56.31 degrees
Hence, the angle of elevation from the boy's eye to the top of the tower is approximately 56.31 degrees.
Once you draw the diagram, you can form a triangle to solve the problem.
For this triangle,
Side 1 = base = distance = 20m
Side 2 = height = (30 - 1.5) = 28.5m
Side 3 = hypotenuse
Angle of elevation = θ
From the diagram,
tanθ = height/base
= 28.5/20
= 1.425
θ = arctan(1.425)
= 54.9 degrees