a man 1.83m tall, stands al a distance of 14.8m away from the base of a tower. he discovers that the angle of elevation of the top of the tower is 63 calculate the height of the tower.
Draw a diagram. If h is the height of the tower, then
(h-1.83)/14.8 = tan63°
Now just solve for h
h=30.88m
Bring the solution to the question
14.8 tan 63= opp
29.0466= opp
Total H = opp + man's height
Total H = 29.05 + 1.83
= 30.88m
A man 1.83m tall stands at a distance of 14.8m away from the base of a tower .he discovers that the angle of elevation of the top of the tower is 63.calculate the height of the tower
To calculate the height of the tower, we can use the tangent of the angle of elevation.
First, let's define the variables:
- h: height of the tower (the value we want to find)
- d: distance from the man to the base of the tower (given as 14.8m)
- a: angle of elevation (given as 63 degrees)
- m: height of the man (given as 1.83m)
We can use the tangent function to relate the angle of elevation with the height of the tower and the distance from the base of the tower:
tan(a) = h / d
Rearranging the equation, we can express the height of the tower:
h = tan(a) * d
Now, let's substitute the known values into the formula and solve for h:
h = tan(63) * 14.8
Using a scientific calculator or trigonometric tables, we find that tan(63) is approximately 2.141.
Plugging in this value, we have:
h = 2.141 * 14.8
Calculating this, we get:
h ≈ 31.7256
Therefore, the height of the tower is approximately 31.7256 meters.