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CHAPTER 10 : ANGLES OF ELEVATION AND DEPRESSION EXERCISE 1

1. Diagram 1 shows a post QR which is vertical to the ground. An observer P looks up at R R

P Q DIAGRAM 1 . Name the angle of elevation concerned.

Answer: ...... ..................

2. In the diagram 2, ADC represents a vertical tower. Given that the angles of elevation of D and C from B are 30o and 50o respectively. C D A B 100m DIAGRAM 2 Calculate the distance from D to C.

Answer: ...... ..................

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DIAGRAM 4

2.5

3. In the diagram 3, PQ and SR are two vertical poles on a horizontal plane.The angle of elevation of R from P is 52º. R DIAGRAM 3 Calculate the value of h.

Answer: ................ 4. In the diagram 4, XY and KLN are vertical poles on a horizontal plane.

The angle of elevation of K from X is

Answer: ................

P

Q S

h m

2 m

K

L

N

X

Y

2

10

4.62

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5. In the diagram 5, BCD represents a vertical pole. The angle of elevation of D from A is 50o. D C

A B 20 m DIAGRAM 5 Calculate the distance from C to D.

Answer: ................ 6. In the diagram 6 PQST is a straight line. R P Q S T

DIAGRAM 6 The angle of depression of Q from R is

20o

160o

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Answer: ................ 7. In the diagram 7, EF and UV are two vertical poles. The angle of elevation of U from F is 32o

while the angle of depression of U from E is 28o. E U F V DIAGRAM 7 Calculate the height of the pole EF in m, correct to 1 decimal place.

Answer: ................ 8. The height of a tower is 400m. A car is parked 250m away from the foot of the tower. Calculate the angle of elevation of the top of the tower from the car.

Answer: ................

9. A bird is flying a height of 800m above sea level. At a particular moment, the horizontal distance between the bird and a ship is 650m. Calculate the angle of depression of the ship from the bird.

4 m

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Answer: ................

10. The diagram 8 shows a vertical wooden structure PQRS erected on a horizontal ground. The angle of the elevation of P from S is 50º. 20 o DIAGRAM 8 Find the angle of depression of S from Q

Answer: ................

R

Q

P

S

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CHAPTER 10 : ANGLES OF ELEVATION AND DEPRESSION EXERCISE 2 1. A point P is 30° from the foot of a flagpole. The angle of elevation of the top of the pole from

P is 25°. Calculate the height of the pole, correct to 2 significant figures.

Answer:……….......

2. A tower is 100 m tall. From the top of the tower, the angle of depression of a car is 50°. Calculate the distance of the car from the base of the building, correct to 2 significant figures.

Answer:……….......

3. A man, who is 1.7 m tall, stands on horizontal ground 30 m from a tree. The angle of elevation of the top of the tree from his eyes is 24°. Calculate the height of the tree, correct to the nearest metre.

Answer:……….......

4. A point P on horizontal ground is 40 m from a building. The angle of depression of X from the top, T, of the building is 60°. Calculate the height of the building.

Answer:………....... 5. In Diagram 1, A and B are two balls 10 m apart on horizontal ground. From the top of a tower, D, the angles of depression of A and B are 35° and 45° respectively .

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. Calculate the height of the tower CD, correct to the nearest metre.

Answer:……….......

D

A 10 m B C

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6. Diagram 2 shows two vertical iron bars, KM and ST. The angle of elevation of S from M is 56° and the angle of depression of T from K is 37°. S K M T 80 m

Diagram 2 Calculate the difference in length between the two iron bars in m..

Answer:………....... 7. Diagram 3 shows two identical lamp posts which are 300 m apart. The angle of elevation of E from A is 45° while the angle of depression of A from G is 71°. E G F H A

Diagram 3 Calculate (a) the height of each lamp post to the nearest metre. (b) the angle of elevation of E from H.

Answer (a):………....... Answer (b):……….......

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8. In Diagram 4, RST is a vertical pole. R S 40 m T U Diagram 4 Find

(a) the angle of elevation R from U. (b) the angle of depression of U from S. (c) the distance between R and S in m.

Answer (a):………....... Answer (b):………....... Answer (c):……….......

9. The diagram 5shows two vertical poles GH and IJ. The angle of elevation of I from H is 36°. I G 5 m 3 m H J

Diagram 5 Find

(a) the horizontal distance between the two poles. (b) The angle of depression of G from I.

Answer (a):………....... Answer (b):……….......

18 o

22 o

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10. The diagram 6 shows 3 vertical sticks, AB, CD and EF. The angles of elevation of C from A and E are 60° and 70° respectively. C A E 3 m B D F 5 m 4 m Diagram 6 Find (a) the height of the two sticks, CD and EF. (b) The angle of depression of F from C.

Answer (a):………....... Answer (b):……….......

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CHAPTER 10 : ANGLES OF ELEVATION AND DEPRESSION

DIAGNOSTIC TEST 1. The angle of depression from a river bank to a sampan is 25o. If the vertical distance from the bank to the sampan is 40m, calculate the horizontal distance between the sampan and the river bank. A. 18.65m B. 29.79m C. 47.67m D. 85.78m 2. T 6 m R 8 m S Diagram 1 In diagram 1, find the angle of elevation from R to T. A. 36o 52’ B. 41o 25’ C. 48o 35’ D. 53o 08’ 3. U V W Diagram 2 In diagram 2, find the angle depression from U to W. A. 30o

B. 44o 36’ C. 45o 34’ D. 135o 34’

10 m

7 m

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4. A bird is at a distance of 50m horizontally from a helicopter. The bird is flying at a height of 60m vertically below the helicopter. Find the angle of depression of the helicopter to the bird. A. 33o 33’ B. 39o 48’ C. 50o 12’ D. 56o 27’ 5. A student is observing a ceiling fan. If the angle of elevation of the student to the fan is 20o and the horizontal distance between the two is 6m, calculate the height of the fan the floor ( ignore the height of the student). A. 2.05m B. 2.18m C. 3.82m D. 5.63m 6. In the diagram 3, PQ and RS are two vertical pillars standing on horizontal ground. The angle of elevation of Q from S is 22°. Q S h m 2 m P 8 m R

Diagram 3 Calculate the value of h.. A. 3.2 B. 19.8 C. 5.2 D. 21.8

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7. In the diagram 4, PTS and QR are two vertical poles on horizontal ground. S T R P Q Diagram 4 The angle of elevation of point S from point R is. A. RST B. SRP C. SQP D. SRT 8. In the diagram 5, PQ and RS are two vertical poles. The angle of depression of P from S is 12°. S P 20 m Q 25 m R Diagram 5 Calculate the height, in m, of the pole PQ. A. 5.31 B. 14.69 C. 14.80 D. 97.62

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9. In the diagram 6, UV and PQ are two vertical poles on a horizontal plane. The angle of depression peak U from peak P is 26°. P U 12 m V 18 m Q Diagram 6 Calculate the height of pole UV. A. 2.49 B. 3.22 C. 4.11 D. 4.18 10. The diagram 7 shows two vertical flag posts, KL and MN, on a horizontal plane. The angle of elevation of vertex M from vertex K is 48°. M K 8 m L N 6 m Diagram 7 Calculate the angle of depression of the foot N from the vertex K. A. 12° 33´ B. 23° 25´ C. 36° 10´ D. 48° 23´