1971-12-15 — Page 29

育教倆華 頁一第張八第一日八廿月十年亥辛辰夏WAH KIU YAT PO

報日僑華y HALL

三期星

日五十月二十年一七九一届公年十六國民華中

1972英文中學會考試題預習專欄 3

文書院主編

數學科

(七)

Mathematics

Lesson (7)

Properties of triangl

Sine

In any triangle A80

sini

Proofi

Draw a perpendicula

CD from 0 to AB.

BinB

PQ

180

103 181

Applying the sine rule,

Sing

100 pin41

ain103 18

sina

2. 79 5 cm

sino·

wind

-100m sin35 18!

#1#103°18!

352

FR

RS

sin ZPKQ

ein PSR

B1A / POR

sin ZRPS

Bin 10 10:

Lat32 10°10')

352 I sin32 x 8in10 10!

5.938cm

Cosine law

2abConc

2000089

20000mA

Arx

x Bin21

.49

352

ght of the Magstaff is 88.49 yd.

Sxample: 5

From a point at the foot of a hill, the elevation of the Bums 1 10 5815, and a man after walking 2000 yd.

op a slop of 32° finds the elevation is 73. FLAd the height of the hill.

Solutions

Sing

imilarly

ove the

sind

AB

AD

Pecofi In triangle

sinc

ABC, drav AD perpendicular to BO.

sin ¿DAC

sin LDCA

(sino lay)

sin LADB

Srempie

To construct a ABC, giy

which is mouter

Solutions

(1) Mat Came

baina

can be drawn :

(11) 2nd Canas, am bain

che-triangle can be

drawn and it is

right angled.

triangle.}

(111) 3rd Case!

two triangles

ABC and ABC

can be drawn.

(iv) 4th Case:

-baina

ABO is the only solution

ABoC is rejected

because it does

not include

which

Bolve the triangle in which

Solutions

arid

2a(bGos0)

2ab Cos

2az

180

73

Bin90

ain58

Find the three angies of the triangle with

sin 139° Bin

GO

and

Solutio

<2- 2 52 + 42-62

GOS ZA

5 x 4

Bin58°15' sin139°

4381

2000

height of the hill is 4381 yd.

Exeroine

(1) Solve the triangle, given

132:

224

4262-52

COB

(2)

1-80

Example

A man walks towards a flagstaff at 4 m.p.h.

At

a certain instance he observed the angle of elevation

of its top to be 10°10' and 3 minutes later it was 32°

Find the height of the flagstaff.

Solution:

RS

distance travelled in 3 min.

I 1760 1

352 yd.

• 41°24′

1010

35 181

352yd.

อ

tower 125 yd. high is on a cliff on the bank"

a river, From the top of the tower the angle of depression of a point on the opposite shors in 28°40′ and from the bane of the tower the angle of depression of the same point is 18°201 Find the width of the river and the height of the cliff,

(3) From P a pilot flies 125 yd. in the direction

20 W and turne back. Through an error,

he then flies 125 yd. in the direction 851 40 8. How far and in what direction must he now fly to Teach" his intended destination P