Wednesday

April 16, 2014

April 16, 2014

Posted by **Anonymous** on Sunday, June 23, 2013 at 8:18am.

- maths -
**MathMate**, Sunday, June 23, 2013 at 9:43amI assume the last sentence is

"What is AD?" since AD2 does not mean much.

Hints:

Use cosine rule to find ∠A, in triangle ABC.

A=arccos((20²+24²-22²)/(2*20*24))

=arccos(41/80)

= 59° (approx.)

Then

Area of triangle ABC

=(1/2)AB.AC.sin(A)

=(1/2)*20*24*(11√39)/80

=33√39

Since AD is angle bisector, the altitudes of D to AB equals that to AC.

Therefore AD divides the area of triangle ABC in ratios of the bases AB and AC. Thus

Area of ΔADC=(33√39)*(24/(20+24))

=18√39

Area of ΔADC can also be found by the trigonometric formula

Area of ΔADC

=AD*AC*sin(A/2) ... since AD bisects A

=>

18√39 = AD * 24 *sin(A/2)

=>

AD=3√39/2sin(A/2)=19 (approx.)

- maths -
**Anonymous**, Sunday, June 23, 2013 at 6:20pmIt is asking for the length of AD squared or AD^2.

- maths -
**MathMate**, Sunday, June 23, 2013 at 8:33pmThe solution is given for AD.

Are you able to calculate AD²?

**Related Questions**

math - If ABC is a triangle with AB=20,BC=22 and CA=24. Let D lie on BC such ...

Maths - ABC is a right angled triangle with ∠ABC=90∘ and side ...

maths-areas - in triangle ABC P, Q AND R ARE the mid points of side AB, BC, CA....

Geometry - Triangle ABC has side lengths AB=8, BC=12 and CA=14. Given that D, E ...

Geometry - Triangle ABC has side lengths AB=8, BC=12 and CA=14. Given that D, E ...

heeeeeeeeeeeeeeeeeeeelp maths - In triangle ABC, points D,E,F are on sides BC,CA...

maths-geomtery - draw a scelene triangle ABC with AB=6cm, BC=9cm and CA =8cm. ...

Geometry - ABC is a right angled triangle with ∠ABC=90∘ and side ...

Geometry - Given: A(3,-1), B(5,2), C(-2,0), P(-3,4), Q(-5,-3), R(-6,2). Prove: ...

Geometry - Given: A(3,-1), B(5,2), C(-2,0), P(-3,4), Q(-5,-3), R(-6,2). Prove: ...