An observer 1.6 m tall is 20root3 away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is: 21.6 m 23.2 m 24.72 m None of these
Question
An observer 1.6 m tall is 20root3 away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is: 21.6 m 23.2 m 24.72 m None of these
Solution
To solve this problem, we can use the tangent of the angle of elevation, which is the ratio of the opposite side (the height of the tower minus the height of the observer) to the adjacent side (the distance from the observer to the tower).
The formula is:
tan(θ) = (height of tower - height of observer) / distance from observer to tower
Given:
- The angle of elevation (θ) is 30°
- The height of the observer is 1.6 m
- The distance from the observer to the tower is 20√3 m
We can plug these values into the formula:
tan(30°) = (height of tower - 1.6 m) / 20√3 m
Solving for the height of the tower gives:
height of tower = tan(30°) * 20√3 m + 1.6 m
We know that tan(30°) = 1/√3, so:
height of tower = (1/√3) * 20√3 m + 1.6 m = 20 m + 1.6 m = 21.6 m
So, the height of the tower is 21.6 m.
Similar Questions
From a point 375 meters away from the foot of a tower, the top of the tower is observed at an angle of elevation of 45deg, then the height (in meters) of the tower is?
The Tower of Pisa is an Italian construction with an angle inclination of 85.976° from the ground.Calculate the height of the Tower if a person standing 3.93 m away from the base of the Tower can see its top directly above their head. Group of answer choices55.86 m54.86 m56.00 m
From a point P on a level ground, the angle of elevation of the top tower is 30deg. If the tower is 100 m high, the distance of point P from the foot of the tower is
Angle of elevation measured for a tower erected over a building from a point of aninstrument located on the ground was 12° and 9° for the top and bottom of the towerrespectively. The height of the tower is 9 m. If the angle at depression of plinth level ofthe building from the same instrument is 4°, calculate the height of the building. (7Marks)
From his eye, which stands 1.63 meters above the ground, Isaac measures the angle of elevation to the top of a prominent skyscraper to be 17degrees ∘ . If he is standing at a horizontal distance of 294 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest hundredth of a meter if necessary.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.