if angle ABC =anglePQR, angleA+angleB=100°, AB=3cm, BC=5cm, then find: coordinates of A (4, 0) then find the coordinates of B and the length of AB
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Answer:
Answer:
The length of AD=\frac{12}{5}=2.4 cmAD=
5
12
=2.4cm
Step-by-step explanation:
Given ΔABC, ∠A=90°, AB=3cm, BC=5cm
AD is perpendicular to BC.
We have to find the length of AD
In ΔADB and ΔCAB
∠ADB=∠BAC (each 90° given)
∠B=∠B (common)
By AA similarity rule, ΔADB~ΔCAB
Hence, corresponding sides are in proportion
\frac{DB}{AB}=\frac{AB}{CB}
AB
DB
=
CB
AB
⇒ \frac{DB}{3}=\frac{3}{5}
3
DB
=
5
3
⇒ DB=\frac{9}{5}DB=
5
9
By Pythagoras theorem in ΔADB
AB^2=AD^2+DB^2AB
2
=AD
2
+DB
2
⇒ 3^2=AD^2+(\frac{9}{5})^23
2
=AD
2
+(
5
9
)
2
⇒ AD^2=9-\frac{81}{25}=\frac{144}{25}AD
2
=9−
25
81
=
25
144
⇒ AD=\frac{12}{5}=2.4 cmAD=
5
12
=2.4cm
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