From the Top of a 7m High Building
Let’s analyze a few patterns before looking into the main topic for today’s blog.
- Finding heights is a pattern.
Given an elevation angle and a point of observation, the tangent ratio helps to determine the tower’s height from the ground. The tower’s height is adjustable via queries.
- Pattern: Tower height when flagstaff is atop.
When given the height of the flagstaff, find the tower’s peak. Remember that the distance between the point of observation and the foot of the rise remains constant. It’s possible to ask to calculate the height or the distance from the base.
- Wind-blown tree pattern
To determine the height of a tree when it breaks by the wind and the broken part of the tree becomes the hypotenuse of a newly formed right-handed triangle where one of the angles appears. It’s possible to ask to calculate the tree’s height or the distance from the high of the broken tree.
- Pattern: Elevation Angle
The tangent ratios help evaluate the angle of elevation when the height of the tower and the point of observation are available.
- Pattern: Shadow Length
The length of the tower/pole’s shadow determines when it is appropriate to give an elevation angle. Remember that as the angles of elevation decrease, the size of the shadow increases. You can inquire about the length of the shadow or the object’s height.
- Cloud height pattern
The trigonometric ratios use the angle of depression to calculate the height of the cloud above the lake when the angle of depression exists. The question will be whether the cloud’s depression angle or high above the lake’s surface.
- Pattern
A tower’s height with two points of observation When two angles of elevation are available, we use the concept that the tower’s height remains constant to calculate the high of the building.
It’s possible to determine the building’s height by asking questions from various angles.
Now coming back to the topic, let’s take an example, from the top of a 7 meters high building, the angle of elevation will be 60°, and the angles of depression will be 45°.
In the above figure, the Height of the tower is 7m.
The angle of elevation is 60°
The angle of depression is 45°
From the given figure,
(Tan 45°) = AB/BC
1= AB/BC
AB=BC= 7m.
(tan 60°) = ED/AD
√3 = ED/7 (AD =BC)
ED = 7√3 m
Height of the tower = ED +CD
7√3 + 7 (AB=CD)
So, the height of the tower will be 19.12 m.