A memorial is V-shaped with equal sides of length 243.25 ft. The angle between these sides measures 121°24'. Find the distance between the ends of the two sides. 121°24 243.25 ft 243.25 ft The distance between the ends of the two sides is ft. (Do not round until the final answer. Then round to the nearest hundredth as needed.)

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A memorial is V-shaped with equal sides of length 243.25 ft. The angle between these sides
measures 121 24'. Find the distance between the ends of the two sides.
121 24'
243.25 ft
243.25 ft
The distance between the ends of the two sides is
ft.
(Do not round until the final answer. Then round to the nearest hundredth as needed.)
Transcribed Image Text:A memorial is V-shaped with equal sides of length 243.25 ft. The angle between these sides measures 121 24'. Find the distance between the ends of the two sides. 121 24' 243.25 ft 243.25 ft The distance between the ends of the two sides is ft. (Do not round until the final answer. Then round to the nearest hundredth as needed.)
Question Help
A memorial is V-shaped with equal sides of length 261.25 ft. The angle
between these sides measures 128 24. Find the distance between the ends
of the two sides.
128°24'
261.25 ft
261.25 ft
According to the law of cosines, the square of a side of a triangle is equal to the sum of the squares of the
other two sides, minus twice the product of those two sides and the cosine of the angle included between
them. To find c, use the following form of the law of cosines.
c? = a? +b? -
- 2ab cos C
Substitute 261.25 for a, 261.25 for b, and 128°24' for C into the law of cosines.
2 = a? +b2 - 2ab cos C
c2 = 261.252 + 261.252 - 2(261.25)(261.25) cos 128°24'
Take the positive square root of each side of the equation. Round the answer to the nearest hundredth.
c2 = 261.25 + 261.252 - 2(261.25)(261.25) cos 128°24'
= /261.25 + 261.252 - 2(261.25)(261.25) cos 128°24'
C 470.42
Use a calculator.
Therefore, the distance between the ends of the two sides is approximately 470.42 ft.
Transcribed Image Text:Question Help A memorial is V-shaped with equal sides of length 261.25 ft. The angle between these sides measures 128 24. Find the distance between the ends of the two sides. 128°24' 261.25 ft 261.25 ft According to the law of cosines, the square of a side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those two sides and the cosine of the angle included between them. To find c, use the following form of the law of cosines. c? = a? +b? - - 2ab cos C Substitute 261.25 for a, 261.25 for b, and 128°24' for C into the law of cosines. 2 = a? +b2 - 2ab cos C c2 = 261.252 + 261.252 - 2(261.25)(261.25) cos 128°24' Take the positive square root of each side of the equation. Round the answer to the nearest hundredth. c2 = 261.25 + 261.252 - 2(261.25)(261.25) cos 128°24' = /261.25 + 261.252 - 2(261.25)(261.25) cos 128°24' C 470.42 Use a calculator. Therefore, the distance between the ends of the two sides is approximately 470.42 ft.
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