CBSE Class 10 Mathematics VBQs Applications Of Trigonometry

Case Study Based Questions

I. Application of Trigonometry—Height of Tree/Tower: Mr. Suresh is an electrician. He receives a call regarding a fault on a pole from three different colonies A, B and C. He reaches one-by-one to each colony to repair that fault. He needs to reach a point 1.3 m below the top of each pole to undertake the repair work. Observe the following diagrams.

Refer to Diagram A

Question. What should be the length of ladder DQ that enable him to reach the required position if the height of the pole is 4 m?
(a) (5√3/7)m
(b) (9√3/5)m
(c) (7√2/5)m
(d) (4√3/5)m
Answer : B

Question. What is the distance of the point where the ladder is placed on the ground if the height of pole is 4 m?
(a) 2.5 m
(b) 3.8 m
(c) 1.56 m
(d) 5.3 m
Answer : C

Refer to Diagram B

Question. Given that the length of ladder is 4 2 m . What is height of pole?
(a) 4(1/2)m
(b) 4√5 m
(c) 5√5 m
(d) 5√3 m
Answer : D

Question. The distance of the point where the ladder lies on the ground is
(a) 3√5 m
(b) 4√2 m
(c) 4 m
(d) 4√7 m
Answer : C

Refer to Diagram C

Question. The angle of elevation of reaching point of ladder at pole, i.e., H, if the height of the pole is 8.3 m and the distance GF is 7√3 m, is
(a) 30°
(b) 60°
(c) 45°
(d) None of these.
Answer : A
 

II. A group of students of class X visited India Gate on an educational trip. The teacher and students had interest in history as well. The teacher narrated that India Gate, official name Delhi Memorial, originally called All-India War Memorial, monumental sandstone arch in New Delhi, dedicated to the troops of British India who died in wars fought between 1914 and 1919.The teacher also said that India Gate, which is located at the eastern end of the Rajpath (formerly called the Kingsway), is about 138 feet (42 metres) in height.

Question. What is the angle of elevation if they are standing at a distance of 42 m away from the monument?
(a) 30°
(b) 45°
(c) 60°
(d) 0°
Answer : B

Question. They want to see the tower at an angle of 60°. The distance where they should stand will be
(a) 25.24 m
(b) 20.12 m
(c) 42 m
(d) 24.25 m
Answer : D

Question. If the altitude of the Sun is at 60°, then the height of the vertical tower that will cast a shadow of length 20 m is
(a) 20√3 m
(b) (20/√3)m
(c) (15/√3)m
(d) 15√3 m
Answer : A

Question. The ratio of the length of a rod and its shadow is 1:1 . The angle of elevation of the Sun is
(a) 30°
(b) 45°
(c) 60°
(d) 90°
Answer : B

Question. The angle formed by the line of sight with the horizontal when the object viewed is below the horizontal level is
(a) corresponding angle
(b) angle of elevation
(c) angle of depression
(d) complete angle
Answer : C
 

III. A satellite flying at a height h is watching the top of the two tallest mountains in Uttarakhand and Karnataka, they are being Nanda Devi (height 7,816 m) and Mullayanagiri (height 1,930 m). The angles of depression from the satellite, to the top of Nanda Devi and Mullayanagiri are 30° and 60° respectively. If the distance between the peaks of two mountains is 1937 km, and the satellite is vertically above the mid-point of the distance between the two mountains.

Question. The distance of the satellite from the top of Nanda Devi is
(a) 1118.29 km
(b) 577.52 km
(c) 1937 km
(d) 1025.36 km
Answer : A

Question. The distance of the satellite from the top of Mullayanagiri is
(a) 1139.4 km
(b) 577.52 km
(c) 1937 km
(d) 1025.36 km
Answer : C

Question. The distance of the satellite from the ground is
(a) 1139.4 km
(b) 566.96 km
(c) 1937 km
(d) 1025.36 km
Answer : B

Question. What is the angle of elevation if a man is standing at a distance of 7816 m away from Nanda Devi?
(a) 30°
(b) 45°
(c) 60°
(d) 0°
Answer : B

Question. If a mile stone very far away from, makes 45° to the top of Mullayangiri mountain. So, find the distance of this mile stone from the mountain.
(a) 1118.327 km
(b) 566.976 km
(c) 1937 km
(d) 1025.36 km
Answer : C