geometry
posted by verenice .
the legs of a right angled triangle are 5 cm and 12cm long. find the lengths, to the tenth, of the segment into which the bisector of the right angle divides the hypotenuse.

Let ABC be the rightangled triangle with angleB = 90°
let the bisector angle B be BD where D is on the hypotenuse AC
We know that AD : DC = areaABD : areaBCD
areaABD = (1/2)(12)(BD)sin45°
areaBCD = (1/2)(5)(BD)sin45°
then areaABD : areaBCD = 12 : 5
so AD = (12/17)(13) = 9.2
and DC = 139.2 = 3.8
Respond to this Question
Similar Questions

Math
If the hypotenuse of a right triangle is 13 and one of its legs is 5, find the area fo the triangle. Answer Choices 20 40 45 30 25 I know a hypotenuse the side of a right triangle opposite the right angle. You can't multiply the hypotenuse … 
math
I have 14 questions and I was wondering if someone could check my answers. This is a do or die situation. If I don't get an A, I may not get to graduate. I really appreciate you taking your time to double check theses for me. Thanks … 
Geometry
The legs of a right triangle are 5cm and 12 cm long. Find the lengths, to the nearest tenth, of the segments into which the bisector of the right angle divides the hypotenuse. 
geometry
An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 5 cm long. A second side of the triangle is 6.9 cm long. Find the longest and shortest possible lengths of the third side of the triangle. … 
Geometry
The altitude of the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 14 and 8. What is the length of the altitude? 
Geometry
In ^DEF, the bisector of <F divides the opposite sides into segments that are 4 and 9in long. The side of the triangle adjacent to the 4 in. segment is 6in long. To the nearest tenth of an inch, how long is the third side of the … 
PLEASE HELP!!!!! (Right Triangle Question)
Point N is on hypotenuse BC of triangle ABC such than angle CAN is 45 degrees. If AC=8 and AB=6, find AN. I did Pythagorean Theorem for triangle ABC, and hypotenuse BC will be 10. I don't know how to continue from there. Oh, I'm also … 
math
The legs of a right triangle are 3 and 4 units long. Find the lengths, to the nearest tenth, of the segments into which the bisector of the right angle divides the hypotenuse. (Hint: Draw a picture of the triangle, label one segment … 
Geometry
The altitude to the hypotenuse of a right triangle ABC divides the hypotenuse into 12mm and 16mm segments. Find the lengths of each of the following. A. The altitude to the hypotenuse B. The shorter leg of angle ABC C. The longer leg … 
geometry
What are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotenuse is 15 units long?