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Find Ab and Bc, If: - Mathematics

Sum

Find AB and BC, if:

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Solution

Let BC = x m

BD = BC + CD = (x + 20) cm

In ΔABD,

tan 30° = `"AB"/"BD"`

`(1)/(sqrt(3)) = "AB"/(x + 20)`

x + 20 = `sqrt(3)"AB"`           .....(1)

In ΔABC

tan 45° = `"AB"/"BC"`

1 = `"AB"/x`

AB = x         ...(2)

From (1)

AB + 20 = `sqrt(3)"AB"`

AB`(sqrt(3)-1) = 20`

AB = `(20)/((sqrt3 - 1))`

= `(20)/((sqrt3 - 1)) xx ((sqrt(3) + 1))/((sqrt(3) + 1))`

= `(20(sqrt(3)+1))/(3 - 1)`

= 27.32cm

From (2)

AB = x = 27.32 cm

Therefore BC = x = AB = 27.32 cm

Therefore, AB = 27.32 cm, BC = 27.32 cm

Concept: Solution of Right Triangles
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 24 Solution of Right Triangles [Simple 2-D Problems Involving One Right-angled Triangle]
Exercise 24 | Q 17.1 | Page 304
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