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Using Pythagoras Theorem Determine the Length of Ad in Terms of B and C Shown in Figure. - Mathematics

Using Pythagoras theorem determine the length of AD in terms of b and c shown in Figure.

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Solution

We have,

In ΔBAC, by Pythagoras theorem

BC2 = AB2 + AC2

⇒ BC2 = c2 + b2

⇒ BC = `sqrt(c^2+b^2)`             ........(i)

In ΔABD and ΔCBA

∠B = ∠B                             [Common]

∠ADB = ∠BAC                     [Each 90°]

Then, ΔABD ~ ΔCBA           [By AA similarity]

`therefore"AB"/"CB"="AD"/"CA"`           [Corresponding parts of similar Δ are proportional]

`rArrc/sqrt(c^2+b^2)="AD"/b`

`rArr"AD"="bc"/sqrt(c^2+b^2)`

Concept: Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 7 Triangles
Exercise 7.7 | Q 9 | Page 120
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