I have two geometry problems left and I'm really stuck on them, please help! :(
1. A park in a subdivision is triangular-shaped. Two adjacent sides of the park are 573 feet and 536 feet. The angle between the sides is 58. To the nearest unit, find the area of the park in square yards.
(options)
a. 14,470 yd
b. 43,410 yd
2. Divers looking for a sunken ship have defined the search area as a triangle with adjacent sides of length 2.75 miles and 1.32 miles. The angle between the sides of the triangle is 35. To the nearest hundredth, find the search area.
(options)
a. 1.04 mi.
b. 1.49 mi.
1. A park in a subdivision is triangular-shaped. Two adjacent sides of the park are 573 feet and 536 feet. The angle between the sides is 58. To the nearest unit, find the area of the park in square yards.
(options)
a. 14,470 yd
b. 43,410 yd
2. Divers looking for a sunken ship have defined the search area as a triangle with adjacent sides of length 2.75 miles and 1.32 miles. The angle between the sides of the triangle is 35. To the nearest hundredth, find the search area.
(options)
a. 1.04 mi.
b. 1.49 mi.
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1) As our answers are in yards first convert from given dimensions in ft
573 / 3 = 191 yd
536 / 3 = 178.67 yd
If we draw a parallelogram with horizontal sides 191 yards long and diagonal sides 178.67 yards long at 58 degrees from horizontal, the area of the unknown triangle will be exactly half the the area of the parallelogram. The area of the parallelogram is the base length multiplied by the distance between the horizontal lines or in this case h = 178.67sin58
A = ½bh
A = ½(191)178.67sin58
A = 14470 sq yds
2) same setup as before. As our answers are in the same units as the question, no conversion is needed.
A = ½bh
A = ½(2.75)1.32sin35
A = 1.04 sq mi
573 / 3 = 191 yd
536 / 3 = 178.67 yd
If we draw a parallelogram with horizontal sides 191 yards long and diagonal sides 178.67 yards long at 58 degrees from horizontal, the area of the unknown triangle will be exactly half the the area of the parallelogram. The area of the parallelogram is the base length multiplied by the distance between the horizontal lines or in this case h = 178.67sin58
A = ½bh
A = ½(191)178.67sin58
A = 14470 sq yds
2) same setup as before. As our answers are in the same units as the question, no conversion is needed.
A = ½bh
A = ½(2.75)1.32sin35
A = 1.04 sq mi