Help I will be marking brainliest!!!
A. 18√3
B. 56√3
C. 36√3
D. 56
Show work, if possible. Thanks❤️
Answers
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Explanation:
We'll need the tangent rule
tan(angle) = opposite/adjacent
tan(R) = TH/HR
tan(30) = TH/54
sqrt(3)/3 = TH/54 ... use the unit circle
54*sqrt(3)/3 = TH .... multiply both sides by 54
(54/3)*sqrt(3) = TH
18*sqrt(3) = TH
TH = 18*sqrt(3) which points to choice A as the final answer
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An alternative method:
Triangle THR is a 30-60-90 triangle.
Let x be the measure of side TH. This side is opposite the smallest angle R = 30, so we consider this the short leg.
The hypotenuse is twice as long as x, so TR = 2x. This only applies to 30-60-90 triangles.
Now use the pythagorean theorem
a^2 + b^2 = c^2
(TH)^2 + (HR)^2 = (TR)^2
(x)^2 + (54)^2 = (2x)^2
x^2 + 2916 = 4x^2
2916 = 4x^2 - x^2
3x^2 = 2916
x^2 = 2916/3
x^2 = 972
x = sqrt(972)
x = sqrt(324*3)
x = sqrt(324)*sqrt(3)
x = 18*sqrt(3) which is the length of TH.
A slightly similar idea is to use the fact that if y is the long leg and x is the short leg, then y = x*sqrt(3). Plug in y = 54 and isolate x and you should get x = 18*sqrt(3). Again, this trick only works for 30-60-90 triangles.
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Write an equation of a line that goes thru the points (-2, 6) & (3, -4)
Answers
Answer:
The equation of the line is;
y = -2x + 2
Step-by-step explanation:
Here, we want to write the equation of the line that passes through the given points
The general form of the equation is
y = mx + b
where m is the slope of the line and b is the y-intercept of the line
Mathematically, to get the slope, we use the slope formula
m = (y2-y1)/(x2-x1)
(x1,y1) = (-2,6)
(x2,y2) = (3,-4)
m = (-4-6)/(3+2) = -10/5 = -2
So the equation is in the form;
y = -2x + b
To get b, we substitute any of the two points
6 = -2(-2) + b
6 = 4 + b
b = 6-4 = 2
The equation of the line is thus;
y = -2x + 2
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Answers
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Step-by-step explanation:
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Answers
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Answers
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
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Answers
Answer:
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Step-by-step explanation:
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Answers
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Answers
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Find the complete question attached
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