<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.
Answer: $427140
Step-by-step explanation:
Firstly, we'll add MP to the profit and this will be:
= Rs 400000 + Rs 20000
= Rs 420000
Since there is a discount of 10%, this will then be:
= 420000 - (10% × 420000)
= 420000 - 42000
= $378000
With a VAT of 13%, then the final price will be:
= $378000 + (13% × $378000)
= $378000 + (0.13 × $378000)
= $378000 + $49140
= $427140
Answer:
13 , 17 and 25 cm.
Step-by-step explanation:
Let the length of the first side be x cm.
Then the second is x+4 and the third is 2x-1 cm long.
As the perimeter = 55 cm we have the equation:
x + x + 4 + 2x - 1 = 55
4x + 3 = 55
4x = 52
x = 13 cm.
1. 25 minutes
2. 41 minutes
3. 21 wheels
4. 7
5. 160
6. 415 miles
A circle is a geometric object that has symmetry about the vertical and horizontal lines through its center. When the circle is a unit circle (of radius 1) centered on the origin of the x-y plane, points in the first quadrant can be reflected across the x- or y- axes (or both) to give points in the other quadrants.
That is, if the terminal ray of an angle intersects the unit circle in the first quadrant, the point of intersection reflected across the y-axis will give an angle whose measure is the original angle subtracted from the measure of a half-circle. Since the measure of a half-circle is π radians, the reflection of the angle π/6 radians will be the angle π-π/6 = 5π/6 radians.
Reflecting 1st-quadrant angles across the origin into the third quadrant adds π radians to their measure. Reflecting them across the x-axis into the 4th quadrant gives an angle whose measure is 2π radians minus the measure of the original angle.
