Question

In the adjoining figure, find the length of AD in terms
of b and c.​

Answer 1

Given : a right angle triangle ABC  right angled at A ,  AD ⊥ BC

AB = c

AC = b

To Find :  length of AD in terms of b and c.​

Solution:

Sin ∠C   = AD/ AC

=> AD  = AC Sin∠C

=> AD =  b Sin∠C

=> AD/b = Sin∠C

Sin ∠B   = AD/ AB

=> AD  = AB Sin∠B

=> AD =  c Sin∠B

=> AD =  cSin(90° - C)

=> AD/c  = Cos∠C

Sin²∠C  + Cos²∠C  = 1

=> (AD/b)² + (AD/c)²  = 1

=>  AD²c²  + AD²b²   =  b²c²

=> AD² (c² + b²) = b²c²

=> AD²  = b²c²/  (c² + b²)

=> AD = bc/√(b² + c²)

AD = bc/√(b² + c²)

Learn More:

Find AD if AB ⊥ BC and DE ⊥ BC, AB=9 units , DE=3 units and AC=25 units

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In figure s and t are the points on the side PQ and PR

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Answer 2

Answer:

$AD = \frac{bc}{ \sqrt{ {b}^{2} + {c}^{2} } }$

Step-by-step explanation:

Refer to the attached image