A man 1.5m tall is 23.5 meters away from a tower of height 25m.from his eyes,find the angle of elevation of the top of the tower
tan(A) = (25-1.5)/23.5
P/B=tan thita. Tan thita =23.5/23.5=1.
Tan 45 degree =1
To find the angle of elevation of the top of the tower, we can use basic trigonometry.
Let's denote the height of the man as h1 (1.5m) and the height of the tower as h2 (25m). The distance between the man and the tower is d (23.5m). We need to find the angle of elevation, which we'll denote as θ.
We can create a right triangle using the height of the man, the height of the tower, and the distance between them. The opposite side of the right triangle is h2 (25m), and the adjacent side is d (23.5m). The angle of elevation θ is the angle opposite to the adjacent side.
To find θ, we can use the arctangent function, often denoted as atan or tan^-1:
θ = atan(h2 / d)
Substituting the values we have:
θ = atan(25 / 23.5)
Now, we can calculate this angle using a scientific calculator or any online calculator. The result should be approximately 45.26 degrees.
Therefore, the angle of elevation of the top of the tower, as seen from the man's eyes, is approximately 45.26 degrees.