1. The length of the hypotenuse is 13 inches. The length of one leg is 5 inches. What is the length of the other leg? 2. A 20-foot ladder is placed against the side of a house. The bottom of the ladder is 12 feet from the house. How high up will the ladder reach on the wall? a + b2 = c2 52 + b2 = 132 25 + b2 = 169 25 - 25 + b2 = 169 - 25 b2 = 144 b = V144 = 12 %3D %3D %3D Answer . 12 inches Answer. 3. Marco drives 18 miles south, turns east, and then drives 24 miles to get from his pet shop to his house. If a new road is built in 'a straight line from Marco's shop to his house, how long will the new road be? (Hint: Draw a right triangle with the information given.) 4. The community van service travels on a 40-mile route west from the airport to downtown. From downtown, the bus goes 30 miles north to the city bus station at Cortland. What is the length of the direct bus trip directly from Cortland back to the airport? (Hint: Draw a picture of the van's route.) Answer Answer

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section: Chapter Questions
Problem 75RE
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Question
Using the Pythagorean Theorem
The Pythagorean Theorem shows the relationship of the lengths of the
sides of a right triangle to each other. This equation shows that the
sum of the squares of the two shorter sides (the legs) equals the
square of the third side (the hypotenuse). The hypotenuse is always
opposite the right angle. Use this formula to find any one side when
you know the other two.
The length of the hypotenuse of a right triangle is 5 feet. The length
of one leg is 3 feet. What is the length of the other leg?
Square the
sides given.
Substitute.
Subtract and find
the square root.
C = 5'
a? + b2 = c2
32 + b2 = 52
9 - 9 + b2 = 25 – 9
b2 = 16
b = V16 = 4
9 + b2 = 25
a = 3'
Find the unknown side in each right triangle.
2. A 20-foot ladder is placed against the
side of a house. The bottom of the ladder
is 12 feet from the house. How high up
will the ladder reach on the wall?
1. The length of the hypotenuse is 13 inches.
The length of one leg is 5 inches. What is
the length of the other leg?
a? + b2 = c2
52 + b2 = 132
25 + b2 = 169
25 - 25 + b2 = 169 - 25
b2 = 144
b = V144 = 12
Answer
12 inches
Answer
4. The community van service travels on a
40-mile route west from the airport to
downtown. From downtown, the bus
goes 30 miles north to the city bus
station at Cortland. What is the length of
the direct bus trip directly from Cortland
back to the airport? (Hint: Draw a
picture of the van's route.)
3. Marco drives 18 miles south, turns east,
and then drives 24 miles to get from his
pet shop to his house. If a new road is
built in a straight line from Marco's shop
to his house, how long will the new road
be? (Hint: Draw a right triangle with the
information given.)
Answer
Answer
37
Transcribed Image Text:Using the Pythagorean Theorem The Pythagorean Theorem shows the relationship of the lengths of the sides of a right triangle to each other. This equation shows that the sum of the squares of the two shorter sides (the legs) equals the square of the third side (the hypotenuse). The hypotenuse is always opposite the right angle. Use this formula to find any one side when you know the other two. The length of the hypotenuse of a right triangle is 5 feet. The length of one leg is 3 feet. What is the length of the other leg? Square the sides given. Substitute. Subtract and find the square root. C = 5' a? + b2 = c2 32 + b2 = 52 9 - 9 + b2 = 25 – 9 b2 = 16 b = V16 = 4 9 + b2 = 25 a = 3' Find the unknown side in each right triangle. 2. A 20-foot ladder is placed against the side of a house. The bottom of the ladder is 12 feet from the house. How high up will the ladder reach on the wall? 1. The length of the hypotenuse is 13 inches. The length of one leg is 5 inches. What is the length of the other leg? a? + b2 = c2 52 + b2 = 132 25 + b2 = 169 25 - 25 + b2 = 169 - 25 b2 = 144 b = V144 = 12 Answer 12 inches Answer 4. The community van service travels on a 40-mile route west from the airport to downtown. From downtown, the bus goes 30 miles north to the city bus station at Cortland. What is the length of the direct bus trip directly from Cortland back to the airport? (Hint: Draw a picture of the van's route.) 3. Marco drives 18 miles south, turns east, and then drives 24 miles to get from his pet shop to his house. If a new road is built in a straight line from Marco's shop to his house, how long will the new road be? (Hint: Draw a right triangle with the information given.) Answer Answer 37
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