1

If image

Find

i) Cos A

(ii)

image

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2

Find the value of each of the following expressions and simplify the answer. (i) sin 60 °(cos 45° + sin 30°), (ii) tan 45 °(4cos 60° ? ?3 tan 30°).

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3

Given the following figure, find the value of h, correct to one decimal place

image

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4

Given that

image

Find :

(i)image

(ii)image

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5

From the top of a building 75 m high, John sees a lorry and a minibus along the road, both being on one side of the building at the angles of depression of 300 and 600 respectively.

(i)Sketch a diagram representing this information.

(ii)Determine the distance between the cars, leaving the answer in surd form.

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6

22. An engineer finds that the angle of elevation of the top of a building from a point on the ground is 25°. She walks along a straight line 30 metres closer to the foot of the building and finds that the angle of elevation is 50°. Determine the height of the building. (Your answer should be correct to one decimal place)

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7

23. From the top of a 200 metres high building, the angle of depression to the bottom of a second building is 20°. From the same point, the angle of elevation to the top of the second building is 10°. Calculate the heigh of the second building correct to 2 decimal places.

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8

    A flagpole is 5 meters high. Find to the nearest cm, the length of its shadow when the elevation of the sun is 600.

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9

In the figure below, AE = 20 m, EB = 20?2m and DAE = 45°.

image

Find:

(a)  The length: DE, AD and AB.

(b)  The area of triangle ABE, leaving the answer in surd form.

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10

23.In a left angled triangle,  image . Find sinimage and cosimage.

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11

18.Without using mathematical tables simplify the expression 

image 

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12

A river with parallel banks is 20 m wide. If P and Q are two points on either side of the river, as shown in the figure below, find the distance PQ.


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13

23.A ladder 12m long leans against the top of vertical wall and makes an angle of 52 degrees with the wall. Find the height of the wall.

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14

A and B are two points on the ground level and both lie west of flagstaff. The angle of elevation of the top of the flagstaff from A is 560 and from B is 430. If B is 28m from the foot of the flagstaff. How far apart are the points A and B?

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15

Find the length marked y in four significant figures, given that DC=20cm.

image

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16

A ladder leans against a wall. If the ladder reaches 12m up the wall and its foot is 9m from the base of the wall, find the length of the ladder.

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17

Given that A and B are complementary angles and sinA = image , find tanB (Leave your answer as an improper fraction).

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18

Figure 2 represents plotting of two stations A and B which are 4,000m apart. T is a stationary target in the same vertical plane as A and B. When the distance from station A is 10,000m, the angle of elevation is 30°.

image

Calculate

(a) The vertical height of the target, TX

(b) The distance AX , BX and TB

(c) The angle of elevation of the target, T , from B

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19

(i) Without using mathematical tables, find the numerical value of

(ii) Write down the equation of the line which passes through (7, 3) and which is inclined at 45° to the positive direction of the x-axis.

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20

If tan A = ¾ and A is acute, find cos A, sin A and hence verify the identity cos2 A + sin2 A =1

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21

A ladder 15m long leans against a vertical wall such that the top of the ladder makes an angle of 63 degrees with the vertical wall. Find the height of the wall.

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22

From the top of a tower which is 50m high, the angle of depression of a car parked on the ground is 30. How far is the car from the base of the tower? Leave the answer in surd form.

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23

The angle of elevation of the top of a tower from a point on the ground 75 metres from the foot of the tower is 25°. Find the height of the tower to the nearest metre.

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24

Given that image where A is an acute angle, find without using mathematical tables the values of :

(i)Cos A

(ii)Tan A

image 

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25

A square tile chose diagonal is 8 cm long makes an angle of 450 with a side of the tile. Evaluate the length of the side of the tile. 

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26

  Without using mathematical tables, find the exact value of 

image 

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