<h3>
Answer: A. 18*sqrt(3)</h3>
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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 <u>choice A</u> 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.
8x-77 would be the answer to this
Answer:3/4
Step-by-step explanation:60 minutes divided by 4 is 15. 3 15 minute increments is 45. 45 minutes is 3 /4 of an hour.
Answer:
x can be cancelled
Step-by-step explanation:
we are given
Firstly, we will factor numerator and denominator
and then we can factor it
now, we can factor denominator
now, we can replace it
we can see that
both terms are having x common
so, x can be cancelled
So,
x can be cancelled
Answer:
The answer would be A. 1 1/5
Step-by-step explanation:
1 8/40 Simplify to 1 1/5
48/40 = 1 8/40
The answer to this question is above.
Hope this helps.
