Answer:
I put the answers in the picture below!
Step-by-step explanation:
Use the Distance Formula and the x-axis of the coordinate plane. Show why the distance between two points on a number line (the
1 answer:
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The time needed to run the second half of the race is 8.44 s
Step-by-step explanation:
The total distance covered by the athlete during the race is
d = 200 m
And the total time taken to cover this distance is
T = 19.19 s
We also know that the time the athlete needs to cover the first half of the race is
Also, we know that
where is the time the athlete takes to cover the second half of the race.
Re-arranging this equation and susbtituting the values, we find the value of t2:
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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°
