Explain WHY a rotation of 180° is the same as doing reflection over the x-axis AND the y-axis?

Mathematics

1 answer:

Effectus [21]2 years ago

4 0

The 180 degree acts like both a horizontal (y axis) and vertical (x axis) reflection in one action.Precisely. Although they appear similar at first,rotating a figure 180 degrees swaps the image left-to-right and top-to-bottom at once.

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The tee for the sixth hole on a golf course is 305 yards from the tee. On that hole, Marsha hooked her ball to the left, as sket

EleoNora [17]

Answer:

Correct answer is option D. 96.4 yd.

Step-by-step explanation:

Please refer to the attached figure for labeling of the given diagram.

ABC is a triangle with the following labeling:

A is the hole, B is the Tee and C is the point where the ball is.

Sides are labeled as:

$a =255\ yd\\c = 305\ yd\\\angle B =17^\circ$

To find:

Side $b = ?$

Solution:

Here, we have one angle and two sides . Third side of the triangle is to be found opposite to the given angle.

We can use cosine formula here to find the value of the unknown side.

$cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}$

Putting all the values:

$cos 17 = \dfrac{255^{2}+305^{2}-b^{2}}{2\times 255\times 305}\\\Rightarrow 0.956 = \dfrac{65025+93025-b^{2}}{155550}\\\Rightarrow 148753.2= 158050-b^{2}\\\Rightarrow b^{2}= 158050-148753.2\\\Rightarrow b^{2}= 9296.795\\\Rightarrow b= 96.42\ yd$