What are two different ways you could find the value of a? Explain these methods. A right triangle is shown. An altitude is drawn from the right angle to the opposite side to form 2 line segments with lengths 9 and 16. The lengths of the other 2 sides are 15 and a.
Solution:
A right triangle is shown.
An altitude is drawn from the right angle to the opposite side to form 2 line segments with lengths 9 and 16.
The lengths of the other 2 sides are 15 and a.
We have to find the value of ‘a’ using two different ways.
The two different methods to find the length of a side in a right-angled triangle are
2. Geometric mean (leg) theorem
By Pythagorean theorem,
(hypotenuse)2 = (base)2 + (altitude)2
a2 = (altitude)2 + (16)2
(20)2 = (altitude)2 + (16)2
400 = (altitude)2 + 256
(altitude)2 = 400 - 256
(altitude)2 = 144
Taking square root,
Altitude = 12
By Geometric mean theorem,
The value of the hypotenuse can be computed as
\(\frac{9+16}{a}=\frac{a}{16}\)
By cross multiplication,
16(25) = a2
a2 = 400
Taking square root,
a = 20
Therefore, the length of the other side a = 20.
What are two different ways you could find the value of a? Explain these methods. A right triangle is shown. An altitude is drawn from the right angle to the opposite side to form 2 line segments with lengths 9 and 16. The length of the other 2 sides are 15 and a.
Summary:
A right triangle is shown. An altitude is drawn from the right angle to the opposite side to form 2 line segments with lengths 9 and 16. The length of the other 2 sides are 15 and a = 20.
