in the right angle triangle ABC, angle B = 90°, D is such a point on AB that AB:BC:BD = root 3:1:1. Find the value of angle ACD
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in the right angle triangle ABC, angle B = 90°, D is such a point on AB that AB:BC:BD = root 3:1:1. Find the value of angle ACD
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Answer:
ACD = 15°
Step-by-step explanation:
In ΔABC
AB : BC : BD = √3 : 1 :1. _____1
In ΔABC
tanC = AB/BC
tanC = √3/1. [Since AB : BC = √3 : 1
from Equation 1]
tanC = √3
But tan60° = √3
therefore C = 60°
Now, in ΔBCD
tanBCD = BD/BC
tanBCD = 1/1. [Since BD:BC = 1/1 from eq 1]
tanBCD = 1
But tan45° = 1
Therefore, BCD = 45°
ACD = ACB - BCD
ACD = 60° - 45°
ACD = 15°
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Answer:
Since, triangle ABC is a right angle triangle.
∴ by pythagoras theorem, we have
side, AC =
(8
2
+6
2
)
= 10 cm