Class 10 Chapter 8

CHAPTER # 8

TEST MATHEMATICS CLASS: 10TH

NAME: _______________

TIME: 20 min

NOTE: Attempt any five questions, 1st two Questions are necessary.

Total Marks: 53,

38

‍دع؏ ل‏ â€ŤŮˆÚŠŘŞŮ†Ř§ŰŒŘŞÚşŰŒŘŞŘ¨ŘłŮ†ŮˆŮ„ŘšŮ…Ů… ل‏ ‍عڊي۔‏ â€ŤŘ°ŮŠŘŤŮ„ŘŤŮ…ŰŒÚŠŘ§Ů…ŘŞŮ… ل‏

ď ś 3 đ??ś đ?œ‘ 5

13 đ?œƒ

B

A

12  Find out all trignometric ratios of above triangle. 3

ď ś Prove that (i)

‍ت‏ â€ŤŘŤŘ§Ř¨Ű’ŰŒŘŹŰŒÚŠŰ ÚŠâ€Ź

(3+3+3+3+3+5)

(sec 2 đ?œƒ − 1) cos 2 đ?œƒ = sin2 đ?œƒ (ii)

(iv) 1 + sin đ?œƒ 1 − sin đ?œƒ =

1 sec 2 đ?œƒ

(v)

cos đ?œƒ sin đ?œƒ

1

= tan đ?œƒ (iii) cos2 đ?œƒ − sin2 đ?œƒ = 2 cos 2 đ?œƒ − 1

1−sin đ?œƒ cos đ?œƒ

cos đ?œƒ = 1+sin (vi) đ?œƒ

csc đ?œƒ −sec đ?œƒ csc đ?œƒ +sec đ?œƒ

=

1−tan đ?œƒ 1+tan đ?œƒ

(vii) csc đ?œƒ = sec 2 đ?œƒ − 1 ‍ت ت‏ ‍ٚ‏ ‍دع؏ ل‏ ‍ذي Ů„ ل‏ â€ŤŘ¨ŮˆŮ„ŘšŮ…Ů… ل‏ ‍عڊي۔‏ ‍لےڊ Ů„ ع‏ â€ŤŮŠŮ‚ÚŠŮŠŮ„Ů„ÚŠŮˆ Ů„ ع‏

ď ś Find out these values without using calculator (3+2) (i) sin 60° cos 30° + cos 60° sin 30° (ii) cos 60° cos 30° + sin 60° sin 30°

ď ś

‍ت‏ ‍ٚ‏ ‍ل‏ ‍لايعمؚب ل‏ â€ŤŮˆŘŞŰŒÚŠŘ§Ř¨Ů…Ů„ŰŒŘŚŮˆŮ„ŘšŮ…Ů…ŘąÚŠÚşŰŒŰ”â€Ź â€ŤŰ’Ű Ű”Ů…ŘŻŘ§Ů†Ű’ÚŠ ع‏ ‍ Ů„ ع‏60â€ŤŮ…ŘŻŘ§Ů†Ű’ÚŠŰ ŘąŘšŮ„ŘśŰŒÚŠŘŻŮ‚Ů…Ř§Řąâ€Ź ‍م‏

5

5

The Length Of Every Side Of A Square Is 60m,Find Out The Length Of Its Diagonal.

ď ś Find out the angle P in the following diagram. 5

ď ś

5

â€ŤŘŻŰŒŰŒŘŚÚŻŮ„ÚŠŘ´ ل‏ â€ŤŮŠŮ…Ř˛Ř§ŮˆŮŠŮ„ đ?‘ƒŮˆŮ„ؚمم ل‏ ‍عڊي۔‏

‍م ت‏ ‍ت‏ ‍ت‏ ‍ت‏ ‍ ŰŒÚŠ Ů‚ Ů„ Ů…ŮˆŮ„ŘšŮ…Ů…ŘąÚŠ لي۔‏x‍( Ů„Ű Ű”â€Źx)m‍( Ř§ŮˆŘąâ€Źx+7)m‍( Ř§ŮˆŘąŘ§Ř§Ů„ŘśŘšâ€Źx+9)m â€ŤŮˆŘŞâ€Ź ‍اڊ ع‏ABCD ‍لاي ستءيللامنڊڞي لم‏

THE diagonal of a rectangular field ABCD is (x+9) m and the sides are (x+7) m and (x) m. find the value of x. ‍ٚ‏ ‍ٚ‏ ‍ٚ‏ â€ŤŮˆŘłŘąŘŹŘ§ÚŠŘ˛Ř§ŮˆŮŠŮ„ ŮˆŘšŘľŘŻŮˆŮ„ŘšŮ…Ů… ل‏ ď ś 5 â€ŤŮ…Ř§Ř¨Ů…Ů„ŮˆŰ Ű”â€Ź ‍ Ů„ ع‏450 â€ŤŮ…Ř§ŮˆŰ’Ú†Ů†ŘŤŘ§ŮˆŘąŘ§ÚŠŘ§ŘłŮŠŮ„â€Ź ‍ Ů„ ع‏300â€ŤŘąÚŠŮŠŰ ÚŠŘ¨ŘŹ لاي‏ Find the measure of angle of elevation of the sun, if a tower 300m high casts a shadow 450m long.

‍ٚ‏

â€ŤŘ§ŮŠŘ§Ű ŮžÚ‘ŰŒŰŒÚŠŮˆÚ†ŰŒŮšŰ’ŘłŘŻŘą Ů„Ř§ŘŤŰ’ÚŠŘ§ŘłŮ„Ř­ŘąŮžŮˆŘ§ŘšŮ‚ ل‏ â€ŤŮ…Ř§ŮˆŰŒÚ†Ů† ل‏ â€ŤŰ’Ű Ű”ŘŻŘą Ů„Ř§ŘŤŰŒÚŠŮˆÚ†Ú‘Ř§ŰŒŘŚ ل‏50Âş â€ŤŰ’Ű Ř§ŮˆŘąŘŻŘą Ů„Ř§ŘŤŰ’ÚŠŘŻŮˆŘąŘłŰ’Ř§Ů†ÚŠŘąŰ’ŘąŮžŘ˛Ř§ŮˆŮŠŮ„ ŘŞŘąŮˆŮ„â€Ź70Âş â€ŤŘ§ŮŠŰ ŘˇŮ‚Ů†Ř§ÚŠŘ˛Ř§ŮˆŮŠŮ„ ŘŞŘąŮˆŮ„â€Ź ď ś â€ŤŘąÚŠŮŠŘ˛ŰŒŮ†ŘŻŘą لا؍اٚچنےڊ‏ ‍ Ů„ ع‏300 5

‍؍اے،ےس Ű’Ů†ŘŞÚŠŘ§Ů Ű’Ů„ŘľŘąŮžŮˆŘ§ŘšŮ‚Ű’Ű Ř&#x;‏

From the top of a hill 300m high, the measure of angle of depression of a point on the nearer shore of the river is 70° and measure of angle of depression of a point directly across the river is 50°.find the width of the river. How far is the river from the foot of hill?

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