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Standard IX

Mathematics

Trigonometric Ratio(sin,cos,tan)

In given figu...

Question

In given figure, AD is the bisector of $∠ A$ . If BD=4 cm, DC=3 cm, and AB= 6 cm, determine AC.

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Solution

In $△ A B C$ , AD is the bisector of $∠ A$ .

$∴$ $\frac{B D}{D C} = \frac{A B}{A C}$

$\Rightarrow$ $\frac{4}{3} = \frac{6}{A C}$

$\Rightarrow$ $4 A C = 18$

$\Rightarrow$ $A C = \frac{9}{2} c m = 4.5 c m$ .

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Similar questions

Q. In given figure, AD is the bisector of

∠ B A C

. If AB=10 cm. AC=14 cm. and BC=6 cm, find BD and DC.

In a $Δ A B C$ , AD is the bisector of $∠ A$ .

(i) If AB = 6.4 cm, AC = 8 cm and BD = 5.6 cm, find DC.

(ii) If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC.

(iii) If AB = 5.6 cm, BD = 3.2 cm and BC = 6 cm, find AC.

(iv) If AB = 5.6 cm, AC = 4 cm and DC = 3 cm, find BC.

Q. In the figure given below

A D

is bisector of

∠ B A C

. If

A B = 6 c m, A C = 4 c m

and

B D = 3 c m

, find

B C

In a $Δ A B C$ , AD is the bisector of $∠ A$ , meeting side BC at D.
(i) If BD= 2.5 cm, AB = 5 cm and AC = 4.2 cm, find DC.
(ii) If BD= 2 cm, AB = 5 cm and DC = 3 cm, find AC.
(iii) If AB= 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.
(iv) If AB =10 cm, AC =14 cm and BC = 6 cm, find BD and DC.
(v) If AC = 4.2 cm, DC = 6 cm and BC = 10 cm, find AB.
(vi) If AD= 5.6 cm, AC = 6 cm and DC = 3 cm, find BC.
(vii) If AB= 3.6 cm, BC e 6 cm and BD = 32 cm, find AC.
(viii) If AB =10 cm, AC = 6 cm and BC = 12 cm, find BD and DC

Q. In a

△

ABC, AD is the bisector of

∠

A, meeting side BC at D.

(i) If BD = 2.5 cm, AB = 5 cm and AC = 4.2 cm, find DC.

(ii) If BD = 2 cm, AB = 5 cm and DC = 3 cm, find AC.

(iii) If Ab = 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.

(iv) If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC.

(v) If AC = 4.2 cm, DC = 6 cm and BC = 10 cm, find AB.

(vi) If AB = 5.6 cm, AC = 6 cmand DC = 3 cm, find BC

(vii) If AD = 5.6 cm, BC = 6 cm and BD = 3.2 cm, find AC

(viii) If AB = 10 cm, AC = 6 cm and BC = 12 cm, find BD and DC.

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In given figure, AD is the bisector of ∠A. If BD=4 cm, DC=3 cm, and AB= 6 cm, determine AC.

In △ABC, AD is the bisector of ∠A. ∴ BDDC=ABAC ⇒ 43=6AC ⇒ 4AC=18 ⇒ AC=92cm=4.5cm.

In given figure, AD is the bisector of $∠ A$ . If BD=4 cm, DC=3 cm, and AB= 6 cm, determine AC.

In $△ A B C$ , AD is the bisector of $∠ A$ .

$∴$ $\frac{B D}{D C} = \frac{A B}{A C}$

$\Rightarrow$ $\frac{4}{3} = \frac{6}{A C}$

$\Rightarrow$ $4 A C = 18$

$\Rightarrow$ $A C = \frac{9}{2} c m = 4.5 c m$ .