7/28/2019 Pythagoras Theorem and Trigonometry Ratios Revision

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Name: ____________________ ( ) Class: ____________ Date: ____________

Revision: Trigonometric Ratios & Pythagoras Theorem

1)In the diagram,BCD is a straight line withAB = 8cm,AC= 6cm,AE= 7cm,ED = 10cm and

Giving your answer correct to 1 decimal place, calculate the length of

(a) AD

(b) BD

2)

The diagram shows in which , ,

and .

(a) Describe Pythagoras Theorem briefly in words.(b) Using Pythagoras Theorem, form an equation inx and show that it reduces to

.

(c) Hence, calculate the perimeter and area of .

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3)

The diagram shows which andBDCis a straight line.

Calculate the value of

(a) x,(b) y.

4) In the diagram,ADCis a straight line and . The lineBD is perpendicular toAC. The

dimensions given are in cm.

(a) Find the area of .

(b) Find the length ofAC, correct to 2 decimal places.(c) Hence or otherwise, calculate the length ofBD, correct to the

nearest whole number.

5)

Find

(i) the length ofAB,

(ii) ,

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(iii) the length ofDC.

6) The diagram shows a right pyramid on a horizontal rectangular base ABCD.Given thatAB = 6 cm, BC= 8 cm and VA = 13 cm,

(i) Find the length ofAC.

(ii) Hence, using the answer in (i), find the height of the pyramid VX.

(iii) Find , in degrees, where Wis the midpoint ofVX.

7)

In the diagram,A,B, C,D are four points in a shape made by 2 right-angled triangles.

AC= 320 m, . Calculate(a) AB,

(b) CD,

(c) .

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10)

From the top of a lighthouse, the angles of depression of two shipsA andB are 30o and

20o respectively. Given that the lighthouse is 40 m high, find the distance between the

two ships.

[Answer Key]

1(a) 12.2 (b) 15.92(a) For any right-angled triangle, the square of the longest side is equal to the sum of the square of the

shorter sides.

(c) 30 cm, 30 cm2

3) (a) 13 cm (b) 8.40 cm

4) (a) 216 (b) 31.38 cm (c) 14 cm5) (i) 1.85 cm (ii) 68.2o (iii) 0.739 m

6) (i) 10 cm (ii) 12 cm (iii)

7) (a) AB = 386 m (b) CD = 155 m (c)

8) (b) (c) 30.9 cm2

9) (i) 300m2 (ii) 29.9m (iii)

10) 40.6 m