The quastion is asking us to determine the measure of angle M in a right triangle LMN. We know that angle N is a right angle and that LM = 76 ( Hypotenuse ) and MN = 40 ( Adjacent ). We will use trigonometry: cos M = Adjacent / Hypotenuse = 40 / 76 = 0.5263158; M = cos^(-1) 0.563158; M = 58.242° = 58° 15`. Answer: The measure of angle M is<span> 58°15`.</span>
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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:
(-∞,∞)
Step-by-step explanation:
The rate of change in this pattern is 2:1 comparing the change in 'y' to the change in 'x'.. this means that if you go form 33 to 51 ( an increase of 18), then the the increase from 16 to ? will be 9. Therefore, ? = 16 + 9 or 25
? = 25
Answer:
y=-|x+1|+1
Step-by-step explanation:
It's an absolute value function vertically flipped and shifted 1 unit to the left, 1 unit to the the top.
