Question

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​

Answer 1

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 2

Answer:

Since, triangle ABC is a right angle triangle.

∴ by pythagoras theorem, we have

side, AC =

(8

2

+6

2

)

= 10 cm