8.2. Applications of the Pythagorean Theorem http://www.ck12.org
- 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
) 2
+
(√
40
) 2
?
(√
194
) 2
98 +40? 194
138 < 194
4 ABCis an obtuse triangle.
- Acute because 7^2 + 82 > 92.
- Right because 14^2 + 482 = 502
Practice
Find the area of each triangle below. Round your answers to the nearest tenth.
1.
2.
3.Find the length between each pair of points.
- (-1, 6) and (7, 2)
- (10, -3) and (-12, -6)
- (1, 3) and (-8, 16)
- What are the length and width of a 42 HDTV? Round your answer to the nearest tenth.
- Standard definition TVs have a length and width ratio of 4:3. What are the length and width of a 42 Standard
definition TV? Round your answer to the nearest tenth.
9.ChallengeAn equilateral triangle is an isosceles triangle. If all the sides of an equilateral triangle ares, find
the area, using the technique learned in this section. Leave your answer in simplest radical form. - Find the area of an equilateral triangle with sides of length 8.
- The two shorter
a. What would be the length of the third side to make the triangle a right triangle?
b. What is a possible length of the third side to make the triangle acute?
c. What is a possible length of the third side to make the triangle obtuse? - The two longer
a. What would be the length of the third side to make the triangle a right triangle?