Solution Manual Trigonometry 5th Edition by Cynthia Y Young With Detailed Chapter Solutions, Answer Key, and Complete Study Resource

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, Section 1.1



43. The length of the longer leg of the given triangle is 3x  12 yards. So,
12 12 3
x   4 3. As such, the length of the shorter leg is 4 3  6.93 yards,
3 3
and the hypotenuse has length 8 3  13.9 yards.

44. The length of the longer leg of the given triangle is 3x  n units. So,
n n 3 n 3
x  . As such, the length of the shorter leg is units, and the
3 3 3
2n 3
hypotenuse has length units.
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45. The length of the hypotenuse is 2x  10 inches. So, x  5. Thus, the length of
the shorter leg is 5 inches, and the length of the longer leg is 5 3  8.66 inches.

46. The length of the hypotenuse is 2x  8 cm. So, x  4. Thus, the length of the
shorter leg is 4 cm, and the length of the longer leg is 4 3  6.93 cm.

47. For simplicity, we assume that the minute hand is on the 12.
Let   measure of the desired angle, as indicated in the diagram below.
Since the measure of the angle formed using two rays emanating from the center
of the clock out toward consecutive hours is always
1
360∘   30∘ , it immediately
12
follows that   4   30∘   120∘ (Negative since measured clockwise.)









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, Chapter 1


48. For simplicity, we assume that the minute hand is on the 9.
Let   measure of the desired angle, as indicated in the diagram below.
Since the measure of the angle formed using two rays emanating from the center
of the clock out toward consecutive hours is always
1
360∘   30∘ , it immediately
12
follows that   5   30∘   150∘ . (Negative since measured clockwise.)




49. The key to solving this problem is setting up the correct proportion.
Let x = the measure of the desired angle.
From the given information, we know that since 1 complete revolution
corresponds to 360∘ , we obtain the following proportion:
360∘ x

30 minutes 12 minutes
Solving for x then yields
 360∘  ∘

x  12 minutes     144 .
 30 minutes 

50. The key to solving this problem is setting up the correct proportion.
Let x = the measure of the desired angle.
From the given information, we know that since 1 complete revolution
corresponds to360∘ , we obtain the following proportion:
360∘ x

30 minutes 5 minutes
Solving for x then yields
 360∘  ∘

x  5 minutes    60 .
 30 minutes 



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