Triangle X Y Z is shown. The length of X Z is 16, the length of Y Z is 12, and the length of Y X is 17. Law of cosines: a2 = b2
2 answers:
Answer:
Therefore A = (0.4338) = 64.29°
Step-by-step explanation:
i) Law of cosines: =
+
– 2bccos(A)
ii) XZ = a = 16 , YZ = b = 12, XY = 17, ∠Y = ∠A
iii) =
+
- (2
12
17
cos(A))
⇒ 256 = 144 + 289 - 408cos(A)
⇒ 256 - 144 - 289 = -408cos(A)
⇒ -177 = -408cos(A)
⇒ cos A = = 0.4338
Therefore A = (0.4338) = 64.29°
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<h3>Answer: 33.75 feet</h3>
In fraction form, this value is equal to 135/4
33.75 ft is equivalent to 33 ft, 9 inches.
===============================================
Explanation:
Refer to the diagram below.
The key point to start with is point H, which is the vertex of the parabola.
Recall that vertex form is
y = a(x-h)^2 + k
What we'll do is plug in the vertex (h,k) = (60,30) which is the location of point H. We'll also plug in (0,45) which is the y intercept, aka the location of point C.
So,
y = a(x-h)^2 + k
y = a(x-60)^2 + 30 .... plug in vertex
45 = a(0-60)^2 + 30 .... plug in y intercept coordinates
45 = a(-60)^2 + 30
45 = a(3600) + 30
45 = 3600a + 30
45-30 = 3600a
3600a = 15
a = 15/3600
a = 1/240
This then means:
y = a(x-h)^2 + k
y = (1/240)(x-60)^2 + 30
This is the equation of our parabola. Plug in x = 30 to determine the height of point K
y = (1/240)(x-60)^2 + 30
y = (1/240)(30-60)^2 + 30
y = (1/240)(-30)^2 + 30
y = (1/240)(900) + 30
y = 15/4 + 30
y = 15/4 + 120/4
y = 135/4
y = 33.75
Therefore, the height of the power line, when it is 30 feet away from one of the poles, is 33.75 feet. This is the y coordinate of point K.
Side note: 33.75 ft = 33 ft + 0.75 ft = 33 ft + 12*0.75 in = 33 ft + 9 inches