Download App

Trigonometric Ratios — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTrigonometric Ratios4 Marks
Question
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 $\alpha=30^{\circ}, \beta=60^{\circ}$.
Image
(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)

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Case study (4 Marks)" from Trigonometric Ratios→Trigonometric Ratios — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

Read the following text carefully and answer the questions that follow: A bird is sitting on the top of a tree, which is $80\ m$ high. The angle of elevation of the bird, from a point on the ground is $45^{\circ}$. The bird flies away from the point of observation horizontally and remains at a constant height. After $2$ seconds, the angle of elevation of the bird from the point of observation becomes $30^{\circ}$. Find the speed of flying of the bird.
Image
$i.$ Find the distance between observer and the bottom of the tree?
$ii$. Find the speed of the bird?
$iii$. Find the distance between second position of bird and observer?
OR
Find the distance between initial position of bird and observer?
→
London eye is an amusement ride consisting of a rotating upright big wheel with multiple passenger-carrying components (commonly referred to as passenger cars, cabins, tubs, capsules, gondolas or pods) attached to the rim in such a way that as the wheel turns, they are kept upright usually by gravity. After taking a ride in London eye, Anu came out from the crowd and was observing her friends who were enjoying the ride. She was curious about the different angles and measures that the wheel will form. She makes a figure as given below.
Image
(i) In Fig. the measure of $\angle R O Q$ is
(a) $60^{\circ}$ $\qquad$ (b) $100^{\circ}$ $\qquad$ (c) $150^{\circ}$ $\qquad$ (d) $90^{\circ}$
(ii) In Fig. 8.33, The measure of $\angle R Q P$ is
(a) $75^{\circ}$ $\qquad$ (b) $60^{\circ}$ $\qquad$ (c) $30^{\circ}$ $\qquad$ (d) $90^{\circ}$
(iii) In Fig. 8.33, the measure of $\angle R S Q$ is
(a) $60^{\circ}$ $\qquad$ (b) $75^{\circ}$ $\qquad$ (c) $100^{\circ}$ $\qquad$ (d) $30^{\circ}$
(iv) In Fig. 8.33, the measure of $\angle O R P$ is
(a) $90^{\circ}$ $\qquad$ (b) $70^{\circ}$ $\qquad$ (c) $100^{\circ}$ $\qquad$ (d) $60^{\circ}$
→
A stable owner has four horses. He usually tie these horses with 7 m long rope to pegs at each corner of a square shaped grass field of 20 m length, to graze in his farm. But tying with rope sometimes results in injuries to his horses, so he decided to build fence around the area so that each horse can graze.
Image
Based on the above, answer the following questions:
(i) Find the area of the square shaped grass field.
(ii) (a) Find the area of the total field in which these horses can graze.
OR
(b) If the length of the rope of each horse is increased from 7 m to 10 m , find the area grazed by one horse. (Use $\pi=3.14$ )
(iii) What is area of the field that is left ungrazed, if the length of the rope of each horse is 7 cm ?
→
Radha, an aspiring landscape designer, is tasked with creating a visually captivating pool design that incorporates a unique arrangement of fountains. The challenge entails arranging the fountains in such a way that when water is thrown upwards, it forms the shape of a parabola. The graph of one such parabola is given below.
Image
The height of each fountain rod above water level is 10 cm. The equation of the downward-facing parabola representing the water fountain is given by
$p(x)=-x^2+5 x-4$
Based on the above information, answer the following questions:
(i) Find the zeroes of the polynomial p(x) from the graph.
(ii) Find the value of x at which water attains maximum height.
(iii)(A) If h is the maximum height attained by the water stream from the water level of the pool, then find the value of h.
OR
(B) At what point(s) on x- axis, the height of water above x- axis is 2 m?
→
The angle of elevation of an aeroplane from a point on the ground is 45°. After a flight of 15 seconds, the elevation changes to 30°. If the aeroplane is flying at a height of 3000 metres, find the speed of the aeroplane.
→
Skysails is that genre engineering science that uses extensive utilization of wind energy to move a vessel in the sea water. The 'Skysails' technology allows the towing kite to gain a height of anything between 100 metres to 300 metres. The sailing kite is made in such a way that it can be raised to its proper elevation and then brought back with the help of a 'telescopic mast' that enables the kite to be raised properly and effectively. In Fig.skysails technology is being used to move a vessel. By observing this figure answer the following questions:
Image
(i) The length of the rope of the kite sail in order to pull the vessel at angle of $30^{\circ}$ and be at a vertic of 200 metre, is
(a) 300 m $\qquad$ (b) 400 m $\qquad$ (c) 500 m $\qquad$ (d) 600 m
(ii) In (i), the length of $B C$ is
(a) $400 \sqrt{3} m$ $\qquad$ (b) $300 \sqrt{3} m$ $\qquad$ (c) $200 \sqrt{3} m$ $\qquad$ (d) $100 \sqrt{3} m$ $\qquad$ 
(iii) If $B C=15$ metre and $\theta=30^{\circ}$, then $A B=$
(a) $2 \sqrt{3} m$ $\qquad$ (b) 15 m $\qquad$ (c) 24 m $\qquad$ (d) $5 \sqrt{3} m$
(iv) If $A B=B C$, then $\theta=$
(a) $0^{\circ}$ $\qquad$ (b) $30^{\circ}$ $\qquad$ (c) $45^{\circ}$ $\qquad$ (d) $60^{\circ}$
→
Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹$ x$ per student and Cricket ₹ y per student. School 'P' decided to award a total of ₹ 9,500 for the two games to 5 and 4 students respectively; while school 'Q' decided to award ₹ 7,370 for the two games to 4 and 3 students respectively.
Image
(i) Represent the following information algebraically (in terms of $x$ and $y$ ).
(ii) What is the prize amount for hockey?
(iii) Prize amount of which game is more and by how much?
(iv) What will be the total prize amount if there are 2 students each from two games?
→
Raman usually go to a dry fruit shop with his mother. He observes the following two situations.
On 1st day: The cost of 2 kg of almonds and 1 kg of cashew was ₹1600.
On 2nd day: The cost of 4 kg of almonds and 2 kg of cashew was ₹3000.
Denoting the cost of 1 kg almonds by x and cost of 1 kg cashew by y, answer the following questions
  1. Linear equations represented by day-I and day -II situations, are
  2. Represent algebraically the situation of day-II.
  3. The linear equation represented by day-1, intersect the x axis at
    Or
    The linear equation represented by day-II, intersect the y-axis at
→
The following TV Tower was built in 1988 and is located in Pitampura, Delhi. It has an observation deck. Observe the picture given below:
Image
The TV Tower stands vertically on the ground. From a point ' $A$ ' on the ground, the angle of elevation of top of the tower (point ' $B$ ') is $60^{\circ}$. There is a point ' $C ^{\prime}$ ' on the tower which is 78 m (approx.) above the ground. The angle of elevation of the point $C$ from point $A$ is found to be $30^{\circ}$.
(i) Draw a well-labelled figure, based on the information given above.
(ii) Find the height of the tower and the distance of the tower from point $A$.
→
A farmer has a field in the shape of trapezium, whose map with scale 1 cm = 20 m, is given below:
The field is divided into four parts by joining the opposite vertices.
Image
Based on the above information, answer any four of the following questions:
1. The two triangular regions AOB and COD are
(a) Similar by AA criterion (b) Similar by SAS criterion
(c) Similar by RHS criterion (d) Not similar
2. The ratio of the area of the $\triangle A O B$ to be area of $\triangle COD$, is
(a) $4: 1$ (b) $1: 4$
(c) $1: 2$ (d) $2: 1$
3. If the ratio of the perimeter of $\triangle A O B$ to the perimeter of $\triangle C O D$ would have been $1: 4$, then
(a) $AB =2 CD$ (b) $AB =4 CD$
(c) $CD =2 AB$ (d) $CD =4 AB$
4. If in $\triangle s A O D$ and $B O C, \frac{A O}{B C}=\frac{A D}{B O}=\frac{O D}{O C}$, then
(a) $\triangle AOD \sim \triangle BOC$ (b) $\triangle AOD \sim \triangle BCO$
(c) $\triangle ADO \sim \triangle BCO$ (d) $\triangle ODA \sim \triangle OBC$
5. If the ratio of areas of two similar triangles $A O B$ and COD is $1: 4$, then which of the following statements is true?
(a) The ratio of their perimeters is $3: 4$ (b) The corresponding altitudes have a ratio $1: 2$
(c) The medians have a ratio $1: 4$ (d) The angle bisectors have a ratio $1: 16$
→