Case study (4 Marks)

Question 14 Marks

Kite festival is celebrated in many countries at different times of the year. In India, every year 14 th January is celebrated as International Kite Day. On this day many people visit India and participate in the festival by flying various kinds of kites. The picture given below, shows kites flying together.

In Fig. the angles of elevation of two kites (Points A and B) from the hands of a man (Point C) are found to be $30^{\circ}$ and $60^{\circ}$ respectively. Taking $A D=50 m$ and $B E=60 m$, find
(i) the lengths of strings used (take them straight) for kites $A$ and $B$ as shown in the figure.
(ii) the distance ' $d$ ' between these two kites.

Answer

(i) $100 m, 40 \sqrt{3} m$
(ii) 121.65 m

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Question 24 Marks

A trolley carries passengers from the ground level located at point $\Lambda$ to up to the top of mountain chateau located at $P$ as shown in Fig. The point $A$ is at a distance of 2000 m from point $C$ at the base of mountain. Here $\alpha=30^{\circ}, \beta=60^{\circ}$.

(i) Assuming the cable is held tight what will be the length of cable?
(a) 2000 m $\qquad$ (b) $2000 \sqrt{3} m$ $\qquad$ (c) $4000 \sqrt{3} m$ $\qquad$ (d) $\frac{4000}{\sqrt{3}} m$
(ii) What will be height of the mountain?
(a) 1000 m $\qquad$ (b) $\frac{2000}{\sqrt{3}} m$ $\qquad$ (c) 2000 m $\qquad$ (d) $2000 \sqrt{3} m$
(iii) What will be the slant height of the mountain?
(a) 4000 m $\qquad$ (b) $\frac{4000}{3} m$ $\qquad$ (c) $4000 \sqrt{3} m$ $\qquad$ (d) $\frac{4000}{\sqrt{3}} m$
(iv) What will be the length of $B C$ ?
(a) 1000 m $\qquad$ (b) $\frac{2000}{3} m$ $\qquad$ (c) $1000 \sqrt{3} m$ $\qquad$ (d) $\frac{1000}{\sqrt{3}} m$

Answer

(i) (d) (ii) (b) (iii) (b) (iv) (b)

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Question 34 Marks

In structural design a structure is composed of triangles that are interconnecting. A truss is one of the major types of engineering structures and is especially used in the design of bridges and buildings. Trusses are designed to support loads, such as the weight of people. A truss is exclusively made of long, straight members connected by joints at the end of each member.

This is a single repeating triangle in a truss system.
(i) In above triangle, what is the length of $A C$ ?
(a) 5 ft $\qquad$ (b) 6 ft $\qquad$ (c) 8 ft $\qquad$ (d) $\frac{8}{\sqrt{3}} ft$
(ii) What is the length of $B C$ ?
(a) $\frac{4}{\sqrt{3}} ft$ $\qquad$ (b) $4 \sqrt{3} ft$ $\qquad$ (c) 8 ft $\qquad$ (d) $8 \sqrt{3} ft$
(iii) If $\sin \Lambda=\sin C$, what will be the length of $B C$ ?
(a) 2 fl $\qquad$ (b) 4 ff $\qquad$ (c) 8 ft $\qquad$ (d) $4 \sqrt{2} ft$
(iv) Which of the following relation will be Irue in the triangle?
(a) $\sin \left(\frac{A+C}{2}\right)=\cos \left(\frac{B}{2}\right)$
(b) $\sin \left(\frac{A+B}{2}\right)=\sin \left(\frac{C}{2}\right)$
(c) $\cos \left(\frac{A+B}{2}\right)=\cos \left(\frac{C}{2}\right)$
(d) $\cos \left(\frac{A-B}{2}\right)=\cos \left(\frac{C}{2}\right)$

Answer

(i) (c) (ii) (b) (iii) (b) (iv) (a)

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Maths Case study (4 Marks)

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