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MissTica
2 years ago
15

Lines b and c are parallel. Horizontal and parallel lines b and c are cut by transversal a. Where line b intersects line a, 4 an

gles are created. Labeled clockwise, from uppercase left, the angles are: (13 x + 9) degrees, 2, 4, 3. Where line c intersects line a, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 6, (5 x + 9) degrees, 8. What is the measure of Angle6?

Geography
1 answer:
lesya [120]2 years ago
3 0

Answer:

  54°

Explanation:

We believe the intended angle numbering is as shown below. This means the marked angles are supplementary, so ...

  (13x +9) +(5x +9) = 180

  18x +18 = 180

  x + 1 = 10

  x = 9

Angle 6 is congruent to (5x+9), so has measure ...

  (5(9) +9) = 54 . . . . degrees

Angle 6 is 54 degrees.

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<h2>Answer:</h2>

This problem can be solved using trigonomtry, assuming that the figure formed by Adam's shadow and Adam himself is a Right Triangle (as shown in the figure attached).


According to this,  the distance from the tip of the shadow to the top of Adam's head is the hypotenuse H of the triangle, and we already know Adam's height and the angle of elevation. So, the trigonometric function that best works in this case is sine:


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Where the opposite leg is the side of the triangle that is opposite to the 60\º angle.

In this especific case:


sen(60\º)=\frac{5.6feet}{H}     (1)


In order to know the value of the hypotenuse we have to find  H from equation (1):

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H=6.4663 feet



Rounding:

H=6.46 feet>>>>>This is the distance from the tip of the shadow to the top of Adam's head



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