Page 169 - Math Course 2 (Book 1)

The Pythagorean Theorem and Its Converse

Mo. 5

Lesson 7 The change in longitude between NASA Ames and
Carson City is | 120 – 122 | or 2 degrees. Let this
distance be a.
KEY CONCEPTS:
1. Use the Pythagorean Theorem. The change in latitude is | 39 – 37 | or 2 degrees
latitude. Let this distance be b.
2. Use the converse of the Pythagorean
Theorem. Use the Pythagorean Theorem to f nd the distance
in degrees from NASA Ames to Carson City,
represented by c.

MO. 5 - L7a
2
2
a + b = c 2 Pythagorean Theorem
The Pythagorean Theorem 2 + 2 = c 2 a = 2, b = 2
2
2
and Its Converse
4 + 4 = c 2 Simplify
THEOREM 5.1 8 = c 2 Add

8 = c Take the positive square root of
Pythagorean Theorem each side.

In a right triangle, the sum of the sequences of the 2.8 ≈ c Use a calculator.
measures of the legs equals the square of the
measure of the hypotenuse. The degree distance between
B
Answer NASA Ames and Carson City is
2
2
Symbols a + b = c 2 c about 2.8 degrees.
a
A b C Find the Length of a Leg

Let’s Begin Example

P 3 cm Q

Find the Length of the Hypotenuse Find d

Example 6 cm d cm

LONGITUDE AND LATITUDE R
2
2
Carson City, Nevada, is located at about 120 (PQ) + (QR) = (PR) 2 Pythagorean Theorem
degrees longitude and 39 degrees latitude. NASA 2 2 PQ = 3, PR = 6
Ames is located about 122 degrees longitude and 3 + d = 62
2
37 degrees latitude. Use the lines of longitude and 9 + d = 36 Simplify.
latitude to f nd the 2 Subtract 9 from each side.
degree distance to d = 27
the nearest tenth of d = 27 Take the positive square
a degree if you were root of each side.
to travel directly from
NASA Ames to d ≈ 5.2 Use a calculator.
Carson City.
Answer d ≈ 5.2 cm

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