CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set B

Applications Of Trigonometry

Then, AC = 3m and ∠ACB = 45º

Then, AB = 1200 m,

∠ACB = 60º and ∠ADB = 45º.

 

Then,AD  = cot 45º = 1

        AB 

=> AD    = 1

     1200

 

= 1 => AD = 1200 m

 

And,  AC  = cot 60º = 1/√3

        AB

=>    AC    = 1/√3

       1200

   

=> AC  = 1200 

               √3

           = 400 3 m.

 

Q.-  A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 7m.At a point on the plane, the angle of elevation of the bottom of the flagstaff is 30º and that of the top of the flagstaff is 45º. Find the height of the tower.

 

Sol. Let AB be the tower and BC be the flagstaff.

Then, BC = 7 m. Let AB = h.

Let O be the point of observation.

Then, ∠AOB = 30º and ∠AOC = 45º.

Now,  OA     = cot45º = 1

         AC 

=> OA = AC = h + 7.

And,  OA   = cot 30º = 3

         AB

=>   OA   = √3

         h

=>  OA = h√3

=> h + 7 = h√3

 

=> h =     7     ×  √3 + 1

           √3 - 1      √3 + 1

 

=> 7( √3 +1)     = 9.562 m

          2

 

More question-

1. If 7x5x3x2 + 3 is composite number? Justify your answer

2. Show that any positive odd integer is of the form 4q + 1 or 4q +3 where q is a positive integer

3. Prove that √2 + √5 is irrational

4. Use Euclid’s Division Algorithms to find the H.C.F of a) 135 and 225 (45)

b) 4052 and 12576 (4)

c) 270, 405 and 315

5. Prove that 5 - 2√3 is an irrational number

6. Find the HCF and LCM of 26 and 91 and verify that LCM X HCF = Product of two numbers (13,182)

7. Explain why 29 is a terminating decimal expansion

23 x 53

8. given that LCM (77, 99) = 693, find the HCF (77, 99) (11)

9. Find the greatest number which exactly divides 280 and 1245 leaving remainder 4 and 3 (138)

10. Prove that √2 is irrational

11. The LCM of two numbers is 64699, their HCF is 97 and one of the numbers is 2231. Find the other (2813)

12. If HCF (6, a) = 2 and LCM (6, a) = 60 then find a (20)

13. Two numbers are in the ratio 15: 11. If their HCF is 13 and LCM is 2145 then find the numbers (195,143)

14. Express 0.363636………… in the form a/b (4/11)

15. Find the HCF 52 and 117 and express it in form 52x + 117y

16. Write the HCF of smallest composite number and smallest prime number

17. Write whether 2√45 + 3√20 on simplification give a rational or an irrational number

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