Aptitude Height And DistancePage 3

17.

Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles. (a)20√3m, 20m (b)28m, 20√3m (c)80m, 20m (d)20m, 80m

Answer!

Answer is: A
BD = width of road = 80 m
Angle ACB = 60 degree
Angle ECD = 30 degree
AB = ED = Height of poles
In Triangle ABC = tan60 = √3 = AB/BC
AB = BC√3 ………….(1)
In Triangle EDC, tan30 = 1/√3 = ED/CD = AB/(80 - BC)
AB = (80 - BC) x 1/√3 ………….(2)
From equation (1) and (2), we get
BC√3 = (80 - BC) x 1/√3
3BC = 80 – BC
4 BC = 80
BC = 20
So, AB = 20√3

18.

A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the canal. (a)10m, 20m (b)30m, 20m (c)10√3m, 10m (d)20m, 10√3m

Answer!

Answer is: C
Width of canal = BC
CD = 20 m
Angle ACB = 60^o
Angle ADB = 30^o
In Triangle ABC, tan60^o = √3 = AB/BC
AB = BC√3
In Triangle ABD, tan30^o = 1/√3 = AB/(BC + 20)
AB = (BC + 20)/√3
BC√3 = (BC + 20)/√3
3BC = BC + 20
2BC = 20
BC = 10 m (Width of Canal)
Height of tower = AB = 10√3 m

19.	From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower. (a)19.124 m (b)7√3 m (c)7 m (d)191.24 m

Answer!

Answer is: D
AB = Height of building = 7 m
Angle ACB = 45^o
Angle EAD = 60^o
In Triangle ABC, tan45^o = 1 = AB/BC
AB = BC = AD = 7 m
In Triangle tan60^o = √3 = ED/AD
ED = 7√3
So, Height of tower = DC + ED = 7 + 7√3
Height of tower = 7(1 + √3) = 7 x 1.732 = 19.124 m

20.	A girl is sitting in the shade under a tree that is 90 ft from the base of a tower. The angle of elevation from the girl to the top of the tower is 35 degrees. Find the height of the windmill.(in feet) (a)40 (b)64 (c)42.64 (d)40.62

Answer!

Answer is: C
Here given the the girl is 90 feet from the tower
The angle of elevation from the girl to the tower is 35 °
Here we want to solve and find the height of the tower
Recall the trigonometry formulas
Here the angle and the adjacent side length is given
So use the formula of tan
tan 35° = opposite / adjacent
tan 35° = h / 90
h = 90 x tan 35°
h = 90 x 0.4738
h = 42.64 feet
Thus the height of the tower is 42.64 feet.

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