CBSE Class 10 Maths (Standard) 2024 · Paper 30/S/1 · Question 36

Some Applications of Trigonometry 4 marks Medium

Due to short circuit, a fire has broken out in New Home Complex. Two buildings, namely X and Y have mainly been affected. The fire engine has arrived and it has been stationed at a point which is in between the two buildings. A ladder at point O is fixed in front of the fire engine. The ladder inclined at an angle

6 0^{\circ}

to the horizontal is leaning against the wall of the terrace (top) of the building Y. The foot of the ladder is kept fixed and after some time it is made to lean against the terrace (top) of the opposite building X at an angle of

4 5^{\circ}

with the ground. Both the buildings along with the foot of the ladder, fixed at 'O' are in a straight line. The height of building Y is

P A = 123

m. Based on the above information, answer the following questions :

(i)Find the length of the ladder.
(ii)Find the distance of the building Y from point 'O', i.e. OA. (iii)(a) Find the horizontal distance between the two buildings. OR (iii)(b) Find the height of building X.

Ladder from O leaning to building Y (60 deg) and building X (45 deg)

(i)Find the length of the ladder.[1]
(ii)Find the distance of the building Y from point 'O', i.e. OA.[1]
(iii)(a)Find the horizontal distance between the two buildings.[2]
(iii)(b)OR Find the height of building X.[2]

Answer

(i) The ladder is

24

m long; (ii)

O A = 12

m; (iii)(a) The buildings are

12 + 122 = 12 (2 + 1) \approx 28.97

m apart; (iii)(b) Building X is

122 \approx 16.97

m high.

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CBSE Class 10 Maths (Standard) 2024 · Paper 30/S/1 · Question 36

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