# Important Questions for Class 10 Chapter 9 - Some Applications of Trigonometry

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Important questions based on NCERT syllabus for Class 10 Chapter 9 - Some Applications of Trigonometry:

Question 1: Two persons are standing on the opposite sides of a tower. They observe the angles of elevation of the top of the tower to be 30∘ and 38∘ respectively. Find the distance between them, if the height of the tower is 50 m.
Solution:

Two persons A and B are standing on the opposite side of the tower TR and height of tower TR = 50 m and angles of elevation with A and B are 30∘ and 38∘ respectively. Let AR = x and RB = y.
Now in right ΔTAR
tan θ = TR/AR
⇒ tan 30∘ = 50x
1/√3 = 50/x
∴ x = 50√(3)m = 86.60 m
Again in right ΔTRB,
tan 38∘ = 50y
⇒ y tan38∘ = 50
y = 50tan 38∘ = 500.7813 = 63.99 or 64.00 m
∴ Distance between A and B
= x + y = 86.60 + 64.00 = 150.60m = 150.6m

Distance between the two people = x + y
In ΔABD
tan 45 = 50/y
= 50/y
y = 50 In ΔABC
tan 30 = 50/x
1/√3 = 50/x
x = 50√3
x + y = 50(√3 + 1)
= 50(2.732) = 136.6 m

Question 2: A ladder is placed along a wall such that its upper end is resting against a vertical wall. The foot of the ladder is 2.4 m from the wall and the ladder is making an angle of 68∘ with the ground. Find the height, upto which the ladder reaches.
Solution:
Let AB be the wall and

AC be the ladder, which is placed against the wall. If foot is 2.4 m away from the wall i.e. CB = 2.4 m
Let AB = x m
In right ΔABC,
tanθ = AB/BC
⇒ tan 68∘ = x/2.4
∴ x = 2.4 × tan 68∘ = 2.4 × 2.4751
=5.94 m

tan 60 = h/20
√3 = h/20
⇒ h = 20√3
= 20(1.732)
= 34.64 m