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Two similar four-sided polygons are shown side by side. The left sides are vertical, the top and bottom sides are horizontal, and the right sides travel down and to the right from the top sides. The polygon on the left has the following labeled sides. The left and top sides are labeled 2 cm. The bottom side is labeled 3 cm. The polygon on the right has the following labeled sides. The left side is labeled 3 cm. The bottom side is labeled x. x = cm

Two similar four-sided polygons are shown side by side. The left sides are vertical, the top and bottom sides are horizontal, and the right sides travel down and to the right from the top sides. The polygon on the left has the following labeled sides. The left and top sides are labeled 2 cm. The bottom side is labeled 3 cm. The polygon on the right has the following labeled sides. The left side is labeled 3 cm. The bottom side is labeled x. x = cm

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Additional Topics In Trigonometry
Section3.2: Law Of Cosines
Problem 1ECP: Find the three angles of the triangle whose sides have lengths a=6 centimeters, b=8 centimeters, and...
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In each case below, the two polygons are similar. (Round your answers to one decimal place.)
(a)
Find the length (in centimeters) of the side labeled x.
Two similar four-sided polygons are shown side by side. The left sides are vertical, the top and bottom sides are horizontal, and the right sides travel down and to the right from the top sides.
  • The polygon on the left has the following labeled sides.
    • The left and top sides are labeled 2 cm.
    • The bottom side is labeled 3 cm.
  • The polygon on the right has the following labeled sides.
    • The left side is labeled 3 cm.
    • The bottom side is labeled x.
x = cm
(b)
Find the length (in feet) of the side labeled x.
Two similar five-sided polygons are shown side by side. Starting from the bottom and traveling clockwise, the sides of both polygons are as follows.
  • The first side is horizontal.
  • The second side travels up and to the right.
  • The third side travels down and to the right, ending halfway between the second side.
  • The fourth side travels up and to the left, ending to the left of where the second and third side meet but to the right of the second side.
  • The fifth side travels down and ends at the right edge of the first side.
The second and third sides of the polygons are labeled as follows.
  • For the polygon on the left, the second side is labeled 2.6 ft and the third side is labeled x.
  • For the polygon on the right, the second side is labeled 6.9 ft and the third side is labeled 5.8 ft.
x = ft 
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Follow-up Question
(a)
Find the length (in centimeters) of the side labeled x.
Two similar four-sided polygons are shown side by side. The left sides are vertical, the top and bottom sides are horizontal, and the right sides travel down and to the right from the top sides.
  • The polygon on the left has the following labeled sides.
    • The left and top sides are labeled 6 cm.
    • The bottom side is labeled 9 cm.
  • The polygon on the right has the following labeled sides.
    • The left side is labeled 9 cm.
    • The bottom side is labeled x.
x = cm
(b)
Find the length (in feet) of the side labeled x.
Two similar five-sided polygons are shown side by side. Starting from the bottom and traveling clockwise, the sides of both polygons are as follows.
  • The first side is horizontal.
  • The second side travels up and to the right.
  • The third side travels down and to the right, ending halfway between the second side.
  • The fourth side travels up and to the left, ending to the left of where the second and third side meet but to the right of the second side.
  • The fifth side travels down and ends at the right edge of the first side.
The second and third sides of the polygons are labeled as follows.
  • For the polygon on the left, the second side is labeled 2.6 ft and the third side is labeled x.
  • For the polygon on the right, the second side is labeled 6.7 ft and the third side is labeled 5.6 ft.
x = ft 
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