1971-11-16 — Page 26

報日僑華

二期星日六十月一十年—七九一居公年十六國民牶中育教僑華

(2) 2 towera A and B, on a leval plane subtend on

angle of 90 at an observer's eye, ha walkm directly towards B a distance of 630 yds and then finds the angle subtended to be 143 241. Find the distance of A from each position of the observer.

育教

僑華

之

物詞新

員舉

頁二第張七第 日九廿月九年亥辛屬夏WAH KIU YAT PO

1972英文中學會考試題預習專欄

堅道英文書院主編

數學科

· MATHEMATIOS

Lesson

Probleme eolvable by analysis into right angled triangle

From geometry, we have the Pythagoras theorem.

wo for a rightmangled triangle. Hence if any two of the thres i sides are given, the third side may be determined. Again, the two acute angles are... complementary, so that if one is given, the other can also be found. Therefore in the solution of right- angled triangle, there are actually only 2 casas to be considerede

(a) When any two sides are given,

(11)

Hhen any one side and one acute angle are give

Let us look at the following examples s—

Fixample 1/

boat sailing against the wind from a PL805. I to a place Z due east of Y takes a course either.

N 64 EDT S 64. E atternately. What is the distance of Z from Y if the boat has to travel 5000 ft.7

Radian meature

Definition i

A radian is an angle subtended at. centre of any circle by an are equal

length to the radius of the oirole.

In our figure, 0 is

radius r unita. If PQ

POQ

Suppose FOQ

Then

360

180°

the centre of the oirola or r unite, then

where

denotes

radia

80

180°

This is the formula connecting

the circular measure (în radiane.

and the sexagesimal meesura

(in degrees) of an angle.

fgolutio

Lat A, B

be the 3 turning poântă.

Lat M, N, be the points where the boat meets the line YZ.

Then A AYX, MN, A CNZ are inon.

From A, B, C, we drop perpendiculara

AP, BQ, OR Zespectively to YZ

Let· YP.

Cafto

NR Then

o.ft.

NOW YA

Ив

NO

"Adding we haver - Yi + MB + NO =

But TA+MB + NO

+ b + 0) sac26 me the ength the journey

( + b + o) #no 26 - 2500 16

2500 Ca=26 St.

2 x 2500 4494: 196

So

A sphere of radius 3 in raste inside a conical funnel, whome axis in vertical; the highest point of the sphere is 22 in. above the vertex of the con Find the angle of the cams.

Let be the vertex

of the code.

Let R be the

dentre of the

aphere

Produce HR to meet

the sphere

again at B. which ia

The highest point

of the sphere. Lot N be the point. where the aphere touches the cone..

A

MNR

Remark

Since a radian is a constant real number, it is taken as a standard unit and the number of radiana contained on any angle is apoken of as ite circular measure, In this system, an angle is usually denoted by a real number the unit being implied.

Length of an arc of a citole radius r subtending angleė radian at its centre

With re

to the adjacent

figure,

Jength of ATC

oircumference.

27

27 radians is

360°)

6闡就行

想

校

長學

國在黎生 文孕嘉會 化育潮

濟博 勢世士

利致屆

: 泡安鸿東書院大耳部,於昨夕七時

一個時代的變化,文化有所改變,選出 風頭,在政治以顺脚英,司下爲公 中國文化究分具有人文宅,阿理性主義的 的想。這一切主義及提高人生發佈的理想,

【場同事萬人國 天 百

起成長活

易族

香林館、吳升博士、沈雪珍博士,家,十號,而開補救於萬一。因此歐美國: 「漢

朱伯奇博士,吳公说,尹致中,張六部,劉哲球:王明、祖銘

向,以六無畏和神,去零取未來的光明」。 台灣嘉業,山山訓導長興業,外國大學 香港陷入私的大车学院外,有兩間公立大學常重大。因爲文化,然後民族復,國家復興 你能式,並安敎授演講。生宙新員學習維、蔡術技能和啓發射國家社會的安任越文化的盛衰,应大學前年努力研究學術的關係非 大會開站,首由彩校亞效制,隨主轉過將聚散。為智的散育方式在刷看大联学生的品德,曾染人才,大學生辦售國米文化的傳演裳,國家: 校友,學生殊附屬星形中英文中學、小學、幼稚 優編帶裡到處總寫上教育,問題。在此我來做的」,帶不獨而全,雙方翻知道融財運,此類的 由以長,嘉湖州士及副導長近会,分別主持,並由德椅及夫人梁鞀芳主持囹誇漫蛋盘,至中降然西方物質文明科學做硬润役,封感到酒油 一句,高台湾柠者邓於中等教育,中午数育品互取人一所民面梯己之所短。 。至於我們主要致郊」的從調,努力再努力,熱門再無門,當溫

銀材袋

問發到

注

有

超,而文化大學校長吳康博士,如微银行做家長一发用區問對方有沒有遇學電視獨和解和

点

蟹培:

要們

全響不

淨的人漢思路明果私相

書院校慶

令人不可思溉的了。

分折與攝的能力。另一方域 熱與物質之母,飛相統病,使能孕育指 高湯育方针,就没落到「小乘」的地步。

時離健康

的道夢罐

Example

A wheel of radius r meter is rotating on its axis

at W radians per second. Find the speed of a point oa the rim.

Length of

Area of a sector subtending♬ circle radius r.

271

Solutions

the centra of

In 1 200.

With reference to the adjacent figure

Area of Sector POQ

Area of the circle

of Sector: POQ

21

Example. 1.

Express 45 13 30" in radian.

Solutioni Late be the

Then

A.

1330"

no of radians in 45

45.225

Let 0 be the centre of the wheel.

A is an arbitrary point on the rim.

When OA turns through: an angle of 2 radian, A moves a distance of

where rim,DA.

OA turns through W radiant.

2T土 In 1 sec A moves a distance of H I

Speed of 4 in Wr. matez/sec)

Breraiso 3

(1) The of a circular sector is 6 in. long, and

the angle of the sector is

the araa of the sector?

zadians What is

In the figure, PQ and RS are eras of concentric ciroles cut off by portions: of two radii P3 and

If PS RQ= 1.in. aro PQ - 5 in aro R33 in.. find the radii of the dirolen and the area

225

0.7893 radi an

Of PQRS"

∙180

Example..2

RS

14"

Evaluato in

0.5714

angle of the cone - 2*

·69° 42′

Exe

1, B are two billiard balls at distances 20", 30. from a perfectly elaatio wall CD. The ball A is atruck along AF and hits B full on the rebound. after travelling altogether 70". Neglecting the size of the balls and assuming that AP, PB make

●qual angles with GD, find the value of AFB. ·

Solution = sin

:Cot

180.

Cos 30 Cot

180

xpress the following angles in terms

(a) 60°

(b) 135

(<)

(11) Express the following angles in asgrouss

T