Math, asked by monalisachaudhari6, 1 month ago

c) in the given figure angle ABC = angle BDC = 90°, given angle ACB = 30° and AB= 12
cm, find
(i) the length of AD
(ii) length of AC
(iii) length of BC

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Answers

Answered by kumarsaurav1497
1

Answer:

Selina solutions

Grade 7

Biology

Mathematics

Physics

Chapters in CONCISE Mathematics - Middle School - 7

Exercises in Pythagoras Theorem

Question 9

Q9) In the given figure, angle ACB = 90° = angle ACD. If AB = 10 m, BC = 6 cm and AD = 17 cm, find :

(i) AC

(ii) CD

Solution:

∆ABD

∠ACB = ∠ACD = 90°

and AB = 10 cm, BC = 6 cm and AD = 17 cm

To find:

(i) Length of AC

(ii) Length of CD

Proof:

(i) In right-angled triangle ABC

BC = 6 cm, AB = 110 cm

According to Pythagoras Theorem,

AB^2=AC^2+BC^2AB

2

=AC

2

+BC

2

10^2=AC^2+6^210

2

=AC

2

+6

2

100=AC^2+36100=AC

2

+36

AC^2=100-36=64\ cmAC

2

=100−36=64 cm

AC^2=64\ cmAC

2

=64 cm

\therefore AC=\ \sqrt{8\times8}=8\ cm∴AC=

8×8

=8 cm

(ii) In right-angle triangle ACD

AD = 17 cm, AC = 8 cm

According to Pythagoras Theorem,

AD^2=AC^2+CD^2AD

2

=AC

2

+CD

2

17^2=8^2+CD^217

2

=8

2

+CD

2

289-64=CD^2289−64=CD

2

225=CD^2225=CD

2

CD=\sqrt{15\times15}=15\ cmCD=

15×15

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