8.2. Applications of the Pythagorean Theorem http://www.ck12.org
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Concept Problem Revisited
To find the length and width of a 52” HDTV, plug in the ratios and 52 into the Pythagorean Theorem. We know that
the sides are going to be a multiple of 16 and 9, which we will calln.
( 16 n)^2 +( 9 n)^2 = 522
256 n^2 + 81 n^2 = 2704
337 n^2 = 2704
n^2 = 8. 024
n= 2. 83Therefore, the dimensions of the TV are 16( 2. 83 ′′)by 9( 2. 833 ′′), or 45. 3 ′′by 25. 5 ′′. If the diagonal isy′′long, it
would ben
√
337
′′
long. The extended ratio is 9 : 16 :√
337.
Vocabulary
The two shorter sides of a right triangle (the sides that form the right angle) are thelegsand the longer side (the
side opposite the right angle) is thehypotenuse. ThePythagorean Theoremstates thata^2 +b^2 =c^2 , where the legs
are “a” and “b” and the hypotenuse is “c”.Acutetriangles are triangles where all angles are less than 90◦.Right
triangles are triangles with one 90◦angle.Obtusetriangles are triangles with one angle that is greater than 90◦.
Guided Practice
- GraphA(− 4 , 1 ),B( 3 , 8 ), andC( 9 , 6 ). Determine if 4 ABCis acute, obtuse, or right.
- Do the lengths 7, 8, 9 make a triangle that is right, acute, or obtuse?
- Do the lengths 14, 48, 50 make a triangle that is right, acute, or obtuse?
Answers:
- This looks like an obtuse triangle, but we need proof to draw the correct conclusion. Use the distance formula to
find the length of each side.