CK-12 Geometry Concepts

http://www.ck12.org Chapter 8. Right Triangle Trigonometry

The triangle is acute.

b)

152 + 142? 21^2

225 +196? 441

421 < 441

The triangle is obtuse.

Watch this video for help with the Examples above.

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CK-12 Foundation: Chapter8ApplicationsofthePythagoreanTheoremB

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. 83

Therefore, the dimensions of the TV are 16( 2. 83 )by 9( 2. 833 ), or 45.3 by 25.5. If the diagonal isylong, 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

1. GraphA(− 4 , 1 ),B( 3 , 8 ), andC( 9 , 6 ). Determine if 4 ABCis acute, obtuse, or right.


2. Do the lengths 7, 8, 9 make a triangle that is right, acute, or obtuse? 3. Do the lengths 14, 48, 50 make a triangle
   that is right, acute, or obtuse?

Answers: