In this page trigonometry practical problem20 we are going to see solution with detailed explanation.
Question 20:
The angle of elevation of a tower at a point is 45 degree. After going 40 m towards the foot of the tower the angle of elevation of the tower becomes 60 degree. Calculate the height of the tower.
here AB represents height of the building.In the right triangle ABC the side which is opposite to angle is known as opposite side(AB),the side which is opposite to 90 degree is called hypotenuse side(AC) and remaining side is called adjacent side (BC). Now we need to find the length of the side AB.
In triangle ABD
tan θ = Opposite side/Adjacent side
tan 60° = AB/BD
√3 = AB/x
AB = x √3 ---- (1)
In triangle ABC
tan θ = Opposite side/Adjacent side
tan 45° = AB/BC
tan 45° = AB/(BD+DC)
1 = AB/(x+40)
x + 40 = AB ---- (2)
(1) = (2)
x √3 = x + 40
x √3 - x = 40
x (√3 -1) = 40
x = 40/(√3 -1)
x = [40/(√3 -1)] x [(√3 +1)/(√3 +1)]
x = [40(√3 +1)] / [(√3)² - 1²]
x = [40(√3 +1)] /2
x = 20(√3 +1)
x = 20(1.732+1)
x = 20(2.732)
x = 54.64 m
AB = 54.64√3
Therefore the height of the tower is 54.64√3 m trigonometry practical problem20 trigonometry practical problem20
Application Problems in Trigonometry |
Solution |
(11) A tower is 100√3 meters high. Find the angle of elevation of its top from a point 100 meters away from its foot.
| |
(12) A string of a kite is 100 meters long and it makes an angle of
60° with horizontal. Find the height of the kite,assuming that there is
no slack in the string. | |
(13) The angle of elevation of the top of a tower at a distance of 130 m from its foot on a horizontal plane is found to be 63°. Find the height of the tower. | |
(14) A ladder is leaning against a vertical wall makes an angle of
20° with the ground. The foot of the ladder is 3 m from the wall.Find
the length of ladder. | |
(15) A kite flying at a height of 65 m is attached to a string inclined at 31° to the horizontal. What is the length of string. | |
(16) The length of a string between a kite and a point on the ground
is 90 m. If the string is making an angle θ with the level ground such
that tan θ = 15/8, how high will the kite be? | |
(17) An aeroplane is observed to be approaching the airpoint. It is at a distance of 12 km from the point of observation and makes an angle of elevation of 50 degree. Find the height above the ground. | |
(18) A balloon is connected to a meteorological station by a cable of
length 200 m inclined at 60 degree . Find the height of the balloon
from the ground. Imagine that there is no slack in the cable. | |
(19) The shadow of a building is 81 m long when the angle of elevation of the sun is 30. Find the height of the building. |