Class 10 Maths · Chapter 9

Some Applications of Trigonometry

43 Class 10 Maths questions on Some Applications of Trigonometry from the NCERT textbook, NCERT Exemplar and CBSE board papers 2026, each with its answer and a step-by-step solution.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 3 of 3

1. Q41 CBSE 2026
   Jigyasa is ​fly fishing in a stream ​sitting at the height of $3.1$ m above the surface ​of water. The fishing rod is $2\sqrt{2}$ m long and the fly ​at the end of the string resting on the surface of water is $5$ m away from the base of the platform on which Jigyasa is sitting. The fishing ​rod makes an angle of $45^{\circ }$ with the horizontal and the string ​which is fully taut makes an angle of $60^{\circ }$ with the horizontal as shown in the given figure. Based on the above information, answer the following questions : (Use $\sqrt{3}=1.7$)

   1. (i)What is the height of the top of the fishing rod above the surface of water ?[1]
   2. (ii)How far is the fly from the point on the surface of water directly below the top of the fishing rod ?[1]
   3. (iii)(a)Find the length of the string when it is fully taut.[2]
   4. (iii)(b)OR : A fish pulled the string such that it makes $30^{\circ }$ angle with the horizontal now. What is the length of the string in this case ?[2]
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   (i) The top of the rod is $5.1$ m above the surface of water; (ii) The fly is $3$ m from the point directly below the rod tip; (iii)(a) The fully taut string is $6$ m long; (iii)(b) At $30^{\circ }$ the string is $10.2$ m long.

   Step-by-step solution →
2. Q42 CBSE 2026
   Elevated water storage tanks ​are built to ​store and ​supply water to nearby colonies. In the diagram given above, $AB$ is an ​elevated water tank and $CD$ is a nearby multistorey building. The building is $54$ ​metres away from the ​water tank. From a window ​($W$) of the building, the angle of elevation of top of the tank is $45^{\circ }$ and angle of depression of its foot ​is $30^{\circ }$.

   1. (i)Write a relation between $d$ (the height of window) and $y$.[1]
   2. (ii)Determine the value of $h$.[1]
   3. (iii) (a)Determine height of the water tank.[2]
   4. (iii) (b)Find the value of $x$ and height of the window above ground level.[2]
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   (i) $\sin 30^{\circ }=\frac{d}{y}$, so $d=\frac{y}{2}$ (equivalently $y=2d$). (ii) $h=54$ m. (iii)(a) Height of the water tank $=h+d=(54+18\sqrt{3})$ m $\approx 85.18$ m. (iii)(b) $x=54\sqrt{2}$ m $\approx 76.37$ m, and the height of the window above the ground $=18\sqrt{3}$ m $\approx 31.18$ m.

   Step-by-step solution →
3. Q43 CBSE 2026
   A flagstaff, $7.32$ m ​long is fitted at the top ​of $10$ m tall building. The flagstaff is supported by the ropes which are tied to the point $P$ on the ground which is $x$ m away ​from the base of the ​building. It is given that $l_1$ is the length of ​rope from point $P$ to the base of the flagstaff and $l_2$ is ​the length of ​rope from point $P$ to the top of flagstaff. Rope $l_1$ makes an angle of $30^{\circ }$ with the horizontal and $\theta$ be the angle which rope $l_2$ makes with the horizontal as shown in the figure. Based on the above information, answer the following questions : (Use $\sqrt{2}=1.4$ ​and $\sqrt{3}=1.732$)

   1. (i)Find the value of $x$.[1]
   2. (ii)Find the measure of angle $\theta$.[1]
   3. (iii)(a)Find the total length of ropes needed to support the flagstaff.[2]
   4. (iii)(b)OR : Which rope is longer $l_1$ or $l_2$ and by how much ?[2]
   Show answer

   (i) $x=10\sqrt{3}=17.32$ m; (ii) $\theta =45^{\circ }$; (iii)(a) The total length of ropes needed is $l_1+l_2=20+24.248=44.248$ m; (iii)(b) Rope $l_2$ is longer than rope $l_1$ by $24.248-20=4.248$ m.

   Step-by-step solution →