Using Pythagoras theorem determine the length of AD in terms of b and c shown in the given figure.
Answers
SOLUTION :
Given :
AB = c and AC= b
In ∆ABC,
BC² = AB² + AC²
[By using Pythagoras theorem]
BC =√c² + b²………..(1)
In ∆ABD and ∆CBA
∠B = ∠B [Common]
∠ADB = ∠BAC [Each 90°]
∆ABD ~ ∆CBA [By AA similarity]
∴ AB/CB = AD/CA
[Corresponding parts of similar triangles are proportional]
c/(√c²+b²) = AD/b
bc = AD× (√c²+b²)
AD = bc /√c²+b²
HOPE THIS ANSWER WILL HELP YOU...
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)
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