Asked by Misaki
The segments formed by the altitude to the hypotenuse of a right triangle are 8 and 10. Find the shorter leg of that triangle.
Help please! I am confused on which formula to use or if I should use the Pythagorean Theorem.
Help please! I am confused on which formula to use or if I should use the Pythagorean Theorem.
Answers
Answered by
Reiny
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.
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.
Answered by
Misaki
Thank you so much!!
Answered by
Reiny
welcome!
Answered by
Anonymous
The segments formed by the altitude
to the hypotenuse of a right triangle
are 8 and 10. Find the shorter leg
of that triangle
to the hypotenuse of a right triangle
are 8 and 10. Find the shorter leg
of that triangle
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