# NCERT Solutions for Class 10 Maths

Find 100% accurate solutions for NCERT Class X Math. All questions have been explained and solved step-by-step, to help you understand thoroughly. Free Download option available!

1.   In right triangle ABC,

Hence, the height of the pole is 10 m.

2.   In right triangle ABC,

3.   In right triangle ABC,

Hence, the lengths of the slides are 3 m and 2√3 m respectively.

4.    In right triangle ABC,

5.    In right triangle ABC,

Hence the length of the string is 40√3 m.

6.    AB = 30 m and PR = 1.5 m

AC  = AB – BC

= AB – PR

= 30 – 1.5

= 28.5 m

In right triangle ACQ,

Hence, the walked towards the building is 19√3 m.

7.    Let the height of the tower be h m. Then, in right triangle CBP,

Putting this value in eq. (i), we get,

The height of the tower is 20(√5 – 1) m. 8.

8.    Let the height of the pedestal be h m.

∴  BC = h m

In right triangle ACP,

= 0.8 (√3 + 1) m

Hence, the height of the pedestal is 0.8 (√3 + 1) m.

9.   Let the height of the building be h m.

10.   In right triangle PRQ,

Also,      BR = 80 – h = 80 – 20 = 60 m

Hence the heights of the poles are 20√3 m each and the distances of the point from poles are 20 m and 60 m respectively.

11.   In right triangle ABC,

Hence height of the tower is 10 √5 m and the width of the canal is 10 m.

12.  In right triangle ABD,

13.   In right triangle ABQ,

Hence the distance between the two ships is 75 (√3 – 1) m. 14.

14.  In right triangle ABC,

Hence the distance travelled by the balloon during the interval is

15.   In right triangle ABP,

∵ Time taken by the car to travel a distance PQ = 6 seconds.

∵ Time taken by the car to travel a distance BQ, i.e.  seconds.

Hence, the further time taken by the car to reach the foot of the tower is 3 seconds.

16.  Let ∠ APB = θ

Then, ∠ AQB =   (90° — θ)

[∠ APB and ∠ AQB are complementary]

In right triangle ABP,

⇒ AB = 6 m

Hence, the height of the tower is 6 m.

Proved.

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