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
Answers
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