Question

Given: ∆ABC, m∠C = 90°
m∠BAC = 2m∠ABC
BC = 24 cm,
AL− ∠ bisector
Find: AL

Answer 1

Answer:

16 un.

Step-by-step explanation:

In right triangle ABC:

m∠C = 90°;

m∠BAC = 2m∠ABC;

BC = 24;

AL is a bisector of angle A.

The sum of the measures of all interior angles in triangle  is always 180°, then

In right triangle the leg that is opposite to tha angle 30° is half of the hypotenuse. This means that

By the Pythagorean theorem,

Let AL be the angle A bisector. By bisector property,

Use the Pythagorean theorem for the right triangle ACL:

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Answer 2

Answer:

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