1

Use the following figure to find the values of x and y .

 

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2

Figure PQR represents a triangular floor such that PQ =QR= 2 cm and angle PQR is 90 . Find PR , correct to two decimal places.

image

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3

In the following figure, AP is perpendicular to BC , AB= 13cm, BP = 5 cm and AC =.15 cm.

image 

Calculate the lengths of AP and CP .

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4

A rectangular frame is made of wooden bars. The diagonal of the frame is 25 cm long and its width is 15 cm. Find the length of the frame.

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5

20. Which of the following triples fits to Pythagoras theorem?

(a) (33, 56, 65)

(b) (15, 30, 35)

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6

.  Find the distance PR in the following figure if the lines PR and RQ are perpendicular.

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7

SECTION B

21. The area of a right-angled triangle is 50cm2. If one of its angles is 45°, calculate the lengths of the sides and the hypotenuse of the triangle.

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8

 if   and angle ABD =  Calculate the length

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9

In the following figure, PQ=17 cm, QS =15 cm, RS= 6 cm and PR = x. Find the value of x

image 

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10

The angle of elevation of the top of a vertical building from a point on the ground is 25°. The point on the ground is 80 m away from the base of the building. By sketching a diagram representing this information, calculate the height of the building.Write the answer correct to one decimal place.

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11

A 4m ladder rests against a vertical wall with its foot 2m from the wall. How far up the wall does the ladder reach? Give your answer in two decimal places.

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12

Use the quadratic formula to solve x2 + 4x ? 12 = 0

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13

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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14

A ladder reaches the top of a wall 18m high when the other end on the ground is 8m from the wall. Find the length of the ladder.

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15

Given the right angled triangle above whose sides are measured in centimeter determine:

  1. the value of x
  2. the area of the triangle (6 marks)
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16

A photograph which has a diagonal of 7.8 cm long is to be fitted in a frame. Show whether the photograph will fit in the frame measuring 6 cm long and 5 cm wide. 

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17

The sides of an equilateral triangle ABC are 10cm each. Find the length marked AD in surd form.

image 

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18

Find the perimeter of a right angled triangle whose base is  imagecm and height is imagecm

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19

A ladder on the ground leans against a vertical wall whose height is 5 metres. The ground distance between the ladder and the wall is 12 metres.

(i) Draw a diagram to represent this information. 

(ii) Using the diagram in part (i), find the length of the ladder.

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