HELP PLZ!!!! When 1480 is divided into 12 equal parts, the remainder is 4. What is a correct way to write the quotient?
1 answer:
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Answer:
a) a = 7.37, b = 15.13, C = 67°
b) 1 triangle
Step-by-step explanation:
<h3>a)</h3>Two angles and one side are given. That means the triangle is uniquely determined, and the remaining sides can be found from the Law of Sines.
The third angle is ...
C = 180° -A -B = 180° -29° -84° = 67°
Then the Law of Sines tells you ...
a/sin(A) = b/sin(B) = c/sin(C)
a = sin(A)/sin(C)·c = sin(29°)/sin(67°)·14 ≈ 7.37
b = sin(B)/sin(C)·c = sin(84°)/sin(67°)·14 ≈ 15.13
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<h3>b)</h3>Ordinarily, when the given angle (B = 30°) is opposite the shorter of the given sides (b = 10 < a = 20), it means there are two possible solutions to the triangle.
However, when the sine of the angle is exactly equal to the ratio of the given sides: sin(30°) = 10/20 = 1/2, the larger angle can only be 90°. That is, the one triangle that can be formed is a right triangle.
The Law of Sines tells you this.
sin(A)/a = sin(B)/b
sin(A) = (a/b)sin(B) . . . . . . multiply by 'a'
A = arcsin(a/b·sin(B)) = arcsin(20/10·sin(π/6)) = arcsin(1)
A = 90°
Answer:
Step-by-step explanation:
We can find the distance using the distance formula:
We then substitute (1,7) as and (-3,-1) as
.
Answer:
B: 50 feet
Step-by-step explanation:
Let A represents the location of the swing, B represents the location of bench and C represents the position of slide,
According to the question,
AB = 100 ft,
BC = 80 ft,
m∠ABC = 30°,
By the cosine law,
Hence, the approximately distance between the swing and the slide is 50 ft.
Option 'B' is correct.
