If

Find

i) Cos A

(ii)

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°).

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

Given that

Find :

(i)

(ii)

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.

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)

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.

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

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

Find:

(a)  The length: DE, AD and AB.

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

23.In a left angled triangle,   . Find sin and cos.

18.Without using mathematical tables simplify the expression 

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.

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.

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?

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

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.

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

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°.

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

(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.

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

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.

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.

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.

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

(i)Cos A

(ii)Tan A

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. 

  Without using mathematical tables, find the exact value of