Cambridge International Mathematics

338 Trigonometry (Chapter 15)

3 Find the measure of all unknown sides and angles in

triangle KLM:

4 The angle of elevation from a point 2 km from the base of the vertical cliff to the top of the cliff

is 17 : 7 o. Find the height of the cliff, in metres.

5 A tangent to a circle from a point 13 cm from the centre is 11 cm in length. Find the angle between

the tangent and the line from the point to the centre of the circle.

6 Without using a calculator, find the value of:

a

sin^230 o

cos^230 o

b sin^260 o+ tan 45o¡cos 0o

7 Two cyclists depart from A at the same time. X cycles in a direction

a How far did X travel in 2 hours?

b How far did Y travel in 2 hours?

c Determine the average speed at which Y has travelled.

8 Three towns P, Q and R are such that Q lies 10 : 8 km southeast of P and R lies

15 : 4 km southwest of P.

a Draw a labelled diagram of the situation.

b Find the distance from R to Q.

c Find the bearing of Q from R.

9 Triangle ABC is equilateral with sides 10 cm long.

Triangle DEF is formed by drawing lines parallel to, and

1 cm away from, the sides of triangle ABC, as illustrated.

Find the perimeter of triangle DEF.

10 The figure alongside is a square-based pyramid in which

all edges are 20 cm in length. Find the angle that:

a AD makes with plane EBCD

b plane ADC makes with plane EBCD.

K

M

L

32 cm

19 cm

a

q

xcm

E

D

C

A

B

M

1cm

AB

C

DE

F

145°

A

N

Y

X

145 ofor two hours at a speed of 42 km per hour. Y cycles due east

and at the end of the two hours is directly north of X.

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Y:\HAESE\IGCSE01\IG01_15\338IGCSE01_15.CDR Tuesday, 7 October 2008 2:28:35 PM PETER