<h3>
Answer: A. 18*sqrt(3)</h3>
=============================================
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
----------------------
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.
It should be acute because if A and B are complementary then B and A added together should be 90 so 90-30=60 and 60 would be an acute angle
I believe the answer is 2 because 1/2 x 4 = 4/2 =2
Answer:
1.375 or 1/38
Step-by-step explanation:
(3/8+2/3)+1/3
(1.04166666667)+1/3
1.375 or 1 3/8
Answer:
see below
Step-by-step explanation:
Putting n=1 into the formulas eliminates the first two choices, since they evaluate to 3.57 and 0.85, respectively, not 4.2.
Putting n=2 into the formula eliminates the third choice, because you know that 4.2(0.15) < 3.57 without even using a calculator.
The only viable choice (and the correct choice) is the last one.
