http://www.ck12.org Chapter 8. Right Triangle Trigonometry
Solution:Set the shorter sides in each triangle equal toaandband the longest side equal toc.
a) 6^2 +( 3
√
5 )^2? 8^2
36 +45? 64
81 > 64
The triangle is acute.
b) 15^2 + 142? 21^2
225 +196? 441
421 < 441
The triangle is obtuse.
Example 3:GraphA(− 4 , 1 ),B( 3 , 8 ), andC( 9 , 6 ). Determine if 4 ABCis acute, obtuse, or right.
Solution: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.
AB=
√
(− 4 − 3 )^2 +( 1 − 8 )^2 =
√
49 + 49 =
√
98 = 7
√
2
BC=
√
( 3 − 9 )^2 +( 8 − 6 )^2 =
√
36 + 4 =
√
40 = 2
√
10
AC=
√
(− 4 − 9 )^2 +( 1 − 6 )^2 =
√
169 + 25 =
√
194
Now, let’s plug these lengths into the Pythagorean Theorem.
(√
98