TRIGONOMETRY

Question 1

Solution

Method 1

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Question 2

If sin x equal cosine x, what is x in radian

 

Solution

sin x = cos x when x = 45^o

45^o in radian is

 

Question 3

Solution

Question

Solve the equation  for all positive value of q less than 360^o

(UME 1980, Question 37)

 

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Show that

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Using Pythagoras

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Using sine rule

 

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Using Pythagoras theorem

 

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Question

If the hypotenuse of a right angle isosceles triangle is 2, what is the length of each of the other sides

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Using Pythagoras

                            

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Using  XYZ in the figure above, find

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Question

The side of a triangle are (x+y), x and (x– y) are respectively, if the cosine of the largest angle is 1/5. Find the value of x

 

 

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The largest side is the BC (with length x + 4)

 

 

 

Question

The length of the sides of a right angled triangle are (3x +1)cm , (3x – 1) and x cm. Find x (UME 1983 Question 16)

 

 

 

 

 

 

 

 

 

 

Using pythagoras theorem

                

 

Question

Without using tables calculate the value of 1 + sec ²30  (UME 1985, Question 34)

 

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In the  XYZ above determine the cosine of angle Z (UME 1986, Question 39)

 

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In triangle PQR, PQ =1cm, QR = 2cm and  =120^o, find the longest side of the triangle (UME 1988, Question 42)

 

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In the figure above  and XY  = 8cm. Calculate YZ

 

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In the figure above, if XZ is 10cm, calculate RY in cm

 

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From the figure above, calculate TH in centimeters (UME 1993 Question 40)

 

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Question

The angle of depression of a boat from the top of a cliff 10m high is 30^o. How far is the boat from the foot of the cliff (UME 1994, Question 37)

 

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Using sine rule

                         

Question

The angle of elevation of a building from a measuring place on the ground is 30^o. If the   building is 40 m high. How far is the instrument from the building (UME 1997, Question 35)

 

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Using cosine rule

             

 

Question

A Schoolboy lying on the ground 30m away from the foot of a water tank tower observes that   the angle of elevation of the tank is 60^o. Calculate the height of the water tank

 

 

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Question

A flagstaff stands on the top of a vertical tower. A man standing 60m away the tower     observes that the angle elevation of the top and bottom of the flagstaff are 64^o and 62^o respectively. Find the length of the flagstaff (UME 1991, Question 39)

 

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Question

The pilot of an aeroplane, flying 10 km above the ground in the direction of a landmark views     that the landmark to have angles of depression of 35^o and 55^o. Find the distance between the            two points  (UME 1989,Question 41)

 

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Question

In the figure below  are in adjacent planes. AB =AC =5cm, BC = 6cm and <ADE =60^o, then AE is equal to ( UME 1978, Question 47)

 

 

 

 

 

 

 

 

 

 

Solution

 

 

 

 

 

 

 

 

 

 

 

 

 

Using pythagoras  theorem

Question

Find x in the diagram below QR = 3, PS = x <PQS =30^o, <PRS =90^o (UME 1979,Question41)

 

 

 

 

 

 

 

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QUESTION

If  , find  

(UME 2008, Question 34 set U03, type A)

Solution

From trigonometry definition

 

 

 

 

 

 

              

Answer: Option A

 

QUESTION

A student sitting on a tower 68 metres high observes his principal’s car at an angle of depression of 20^o. How far is the car from bottom of the tower to the nearest metres?

(a) 184m   (b) 185m   (c)  186m  (d)  187m (UME 2008 Question 35, type A SetU03)

SOLUTION

 

 

 

 

 

 

 

 

                                     

                                     

To the nearest metres, AB =187m

Answer: Option D

 

Question

Find the value of sin 45^{o­­­­­­­­­} – cos 30^o

(UME 2009 Question 34, SetU03)

Solution

                                     

Answer: option D

 

Question

A cliff on the bank of a river is 300metres hig. If the angle of depression of a point on the           opposite side is 60^o, find the width of the river (a)  100m   (b)  75  m  (c)  100   (d)  200  m

(UME 2009, Question 34 set U03)

 

Solution

 

 

 

 

 

                                     

Answer: Option C