A man 1.5m tall is 15m away from a tower 20m high.What is the angle of elevation of the top of the tower from his eyes?
Need answer for the mention question.
Make a sketch , complete the triangle
draw a horizontal from the top of the man to the tower, then
tanØ = 18.5/15
Ø = appr 50.96°
Well, let's do some calculations. Since the man is 1.5m tall and 15m away from the tower, we can think of the situation as if the man's height were really close to zero. Now, we just need to figure out the angle of elevation.
Let's call the angle of elevation "x". Now, we have a right-angled triangle, with the height of the tower being the opposite side, and the distance between the man and the tower being the adjacent side. So, we can use the tangent function:
tan(x) = opposite/adjacent
tan(x) = 20m/15m
Now, let me consult my trusty calculator to find the exact value for you... And voila! The angle of elevation is approximately 53.13 degrees.
Just remember, though, this doesn't account for the curvature of the Earth, atmospheric refraction, or whether there's a bird perched on the man's head! So, take it with a pinch of clown-colored salt.
50.93
45
To find the angle of elevation, we need to use trigonometry. The angle of elevation is the angle between the line of sight to the top of the tower and the horizontal line from the observer's eyes.
In this case, we have a right triangle formed by the observer, the top of the tower, and the base of the tower. The vertical leg of the triangle is the height of the tower (20m), and the horizontal leg is the distance from the observer to the tower (15m). The hypotenuse of the triangle is the line of sight from the observer to the top of the tower.
Using the tangent function, we can solve for the angle of elevation, which is equal to the inverse tangent of the height of the tower divided by the distance to the tower:
Angle of Elevation = arctan(height of tower / distance to tower)
Plugging in the values:
Angle of Elevation = arctan(20 / 15)
Using a scientific calculator in degree mode, we can find the angle of elevation.
Please note that the angle of elevation is rounded to the nearest degree.