Access Answers for SAT Maths Chapter 9 – Some Applications
of Trigonometry
Exercise 9.1
1. A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a
vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the
ground level is 30°. (see fig. 9.11)
Solution:
Length of the rope is 20 m and angle made by the rope with the ground level is 30°.
Given: AC = 20 m and angle C = 30°
To Find: Height of the pole
Let AB be the vertical pole
In right ΔABC, using sine formula
sin 30° = AB/AC
Using value of sin 30 degrees is ½, we have
1/2 = AB/20
AB = 20/2
AB = 10
Therefore, the height of the pole is 10 m.
2. A tree breaks due to storm and the broken part bends so that the top of the tree touches the
ground making an angle 30° with it. The distance between the foot of the tree to the point where
the top touches the ground is 8 m. Find the height of the tree.
Solution:
Using given instructions, draw a figure. Let AC be the broken part of the tree. Angle C = 30°
BC = 8 m
To Find: Height of the tree, which is AB
, From figure: Total height of the tree is the sum of AB and AC i.e. AB+AC
In right ΔABC,
Using Cosine and tangent angles,
cos 30° = BC/AC
We know that, cos 30° = √3/2
√3/2 = 8/AC
AC = 16/√3 …(1)
Also,
tan 30° = AB/BC
1/√3 = AB/8
AB = 8/√3 ….(2)
Therefore, total height of the tree = AB + AC = 16/√3 + 8/√3 = 24/√3 = 8√3 m.
3. A contractor plans to install two slides for the children to play in a park. For the children below
the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at
an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a
height of 3m, and inclined at an angle of 60° to the ground. What should be the length of the slide
in each case?
Solution:
As per contractor’s plan,
of Trigonometry
Exercise 9.1
1. A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a
vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the
ground level is 30°. (see fig. 9.11)
Solution:
Length of the rope is 20 m and angle made by the rope with the ground level is 30°.
Given: AC = 20 m and angle C = 30°
To Find: Height of the pole
Let AB be the vertical pole
In right ΔABC, using sine formula
sin 30° = AB/AC
Using value of sin 30 degrees is ½, we have
1/2 = AB/20
AB = 20/2
AB = 10
Therefore, the height of the pole is 10 m.
2. A tree breaks due to storm and the broken part bends so that the top of the tree touches the
ground making an angle 30° with it. The distance between the foot of the tree to the point where
the top touches the ground is 8 m. Find the height of the tree.
Solution:
Using given instructions, draw a figure. Let AC be the broken part of the tree. Angle C = 30°
BC = 8 m
To Find: Height of the tree, which is AB
, From figure: Total height of the tree is the sum of AB and AC i.e. AB+AC
In right ΔABC,
Using Cosine and tangent angles,
cos 30° = BC/AC
We know that, cos 30° = √3/2
√3/2 = 8/AC
AC = 16/√3 …(1)
Also,
tan 30° = AB/BC
1/√3 = AB/8
AB = 8/√3 ….(2)
Therefore, total height of the tree = AB + AC = 16/√3 + 8/√3 = 24/√3 = 8√3 m.
3. A contractor plans to install two slides for the children to play in a park. For the children below
the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at
an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a
height of 3m, and inclined at an angle of 60° to the ground. What should be the length of the slide
in each case?
Solution:
As per contractor’s plan,
