# 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