Mathematics: Given: ∆abc, m∠c = 90° m∠bac = 2m∠abc bc = 24 cm, al− ∠ bisector find: al

Step-by-step explanation:(4i)^4 - (2i)^2256 + 2 = 258...

Given: ∆abc, m∠c = 90° m∠bac = 2m∠abc bc = 24 cm,

misa11234

15.03.2022

AL=24 cm

Step-by-step explanation:

We are given that a triangle ABC,

$m\angle C=90^{circ}$

$m\angle BAC=2m\angle ABC$

BC=24 cm

AL is angle bisector

We have to find the value of AL

Let $m\angle ABC=x$

In triangle ABC

$m\angle BAC+m\angle ABC+m\angle ACB=180^{\circ}$

2x+90+x=180

3x=180-90

3x=90

$x=\frac{90}{3}=30$

$m\angle ABC=30^{\circ}$

$m\angle BAC=2\times 30=60^{\circ}$

AL is a bisector of angle A

Then $m\angle CAL=30^{\circ}$

BL=LC=12 cm

In triangle ACL

$sin\theta =\frac{perpendicular side }{hypotenuse}$

$sin30^{\circ}=\frac{12}{AL}$

$\frac{12}{AL}=\frac{1}{2}$

$AL=12\times 2=24 cm$

Hence, AL=24 cm

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