Question

What is the length of the altitude drawn to the hypotenuse?

Answer 1

well the problem needs ratios of corresponding sides in similar triangles.

Answer 2

I thin u mean the length of AB

Answer 3

Am I right ...?

Answer 4

Yes, the length of AB.

Answer 5

Here's how to do this one,
consider the triangle ADC and ABC
angle A = angle B = 90 degree
angle C is common
angle D = angle CAB (remaining angle)
there for triangle ADC and ABC r similar (AAA)

consider the triangle ADC and ABD
angle A = angle ABD = 90 degree
angle D is common
angle C = angle BAD (remaining angle)
there for triangle ADC and ABC r similar (AAA)

so tri. ADC = tri. ABC
tri. ADC = tri. ABD

therefor tri.ABC = tri.ABD
considering the 2 triangle ABC and ABD
11/AB = AB/13 Corresponding sides of congruent triangle)

Now solve it and u could find the length of AB
hope this will help ya!

Answer 6

use the fact that

\[\cot(90 - \alpha) = \tan(\alpha) \]

therefore the ratios are

\[\frac{13}{AB} = \frac{AB}{11}\]

so \[AB^2 = 143\]

Answer 7

Awesome! thanks so much everyone :)

Answer 8

u r welcome

Answer 9

but you need to similarty proof, by Angle Angle Postulate