The segments formed by the altitude to the hypotenuse of a right triangle are 8 and 10. Find the shorter leg of that triangle.

Question

Help please! I am confused on which formula to use or if I should use the Pythagorean Theorem.

Answer 1

Make a sketch of a right-angled triangle ABC with angleB = 90°
Draw in the altitude from C to hypotenuse AC to meet it at D.
You now have 3 similar right-angled triangles. (easy to see by considering the angles)

I will list them, with corresponding vertices in the same column
ABC
ADB
BDC

Using the last two:
AD/DB = BD/DC
BD^2 = ADxDC
BD^2 = 10(8) = 80

Now in the smaller triangle
BD^2 + DC^2 = BC^2
80 + 64 = BC^2
BC = √144 = 12

If needed, you can find any of the remaining sides and any of the angles.

Answer 2

Thank you so much!!

Answer 3

welcome!

Answer 4

The segments formed by the altitude
to the hypotenuse of a right triangle
are 8 and 10. Find the shorter leg
of that triangle