Geometry
posted by Ashley
in triaangle ABC, AB=20 cm, AC=15 cm the length of the altitude AN is 12 cm prove that ABC is a right triangle
so far i got that angle ANC is 90 degrees by definition on altitude i got really confused after so can you show me how to answer the question and the soulotion please.

Reiny
I will assume that N is on BC.
So you have two rightangled triangles, BNA and CNA.
In BNA, BN^2 = 20^2  12^2 , so
BN = 16
in CNA, CN^2 = 15^2  12^2
CN = 9
so BC = 25 , and
25^2 = 20^2 + 15^2
so by Pythagoras, we have right angle at A 
Anonymous
I think its Pythagorean, but thanks I had the same problem for Rsm homework
Respond to this Question
Similar Questions

Geometry how to write proof
ABC is a right triangle. Angle C is 90 degree. Altitude CD is drawn to hypotenuse AB. Prove AB/BC = BC/BD and AB/AC = AC/AD This is a theorem. How do I prove it? 
geometry
the vertices of triangle ABC are A(1,7)B(9,3)C(3,1) a.prove that the triangle is a right triangle b.which angle is the right angle? 
geometry
In the diagram below, the length of the legs AC and BC of right triangle ABC are 6cm and 8cm, respectively.Altitude CD is drawm to the hypotenuse of triangle ABC. what is the lenght of AD to the nearest tenth of a centimeter? 
Math(Geometry)
In the diagram below(no diagram but details will be provided), right triangle ABC and line BD is an altitude to side line AC. * Prove that (AB)^2=(AC)(AD) When you label the triangle B should be were the right angle is C should be … 
geometry proofs
given ABC is a triangle. Ad is the altitude to BC. Ad biscects angle BAC. Prove: Ad is the median to BC 
Geometry
In the diagram below, the length of the legs AC and BC of right triangle ABC are 6 cm and 8 cm, respectively. Altitude CD is drawn to the hypotenuse of △ABC. What is the length of AD to the nearest tenth of a centimeter? 
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
I have right triangles I need to solve. Can you see if I am doing them correctly or screwed up..1) Rt < is in left corner C: Opposite is 60 deg< A, last angle is at top 30 deg <. line segment of AB is 10. Hypo is f. I got … 
geometry
The altitude of equilateral triangle ABC is 15. What is the length of a side of triangle ABC? 
Math
Which of the following values best approximates of the length of c in triangle ABC where c = 90(degrees), b = 12, and B = 15(degrees)?