Geometry Problem: Find Measure of HG & X-Axis Angle

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In summary, The conversation is about a review problem involving a circle and a point on the circle. The question asks for the measure of an angle formed by a line segment and the x-axis. The answer is 30 degrees and the person is struggling to arrive at this answer. They decide to use trigonometric functions to solve the problem.
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I have a test tomorrow and this is one of my review problems.
"Circle G is centered at the origin with radius 2. Point H is on the circle at (radical 3, 1). What is the measure of the angle formed by HG and the x-axis?" My teacher told me the answer is 30 degrees, and after much trial with this, I have no idea how to arrive at this answer. PLEASE help as this will most likely be on my test tomorrow!
Thanks,
 
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  • #2
on second thought, I'll use trig functions to solve. I think this should work.
 
  • #3
Yes, it's elementary trig. Think of the tangent of the angle.
 

1. What is the HG in a geometry problem?

HG represents the hypotenuse, which is the longest side of a right triangle. It is opposite the right angle and is the side that is directly across from the 90 degree angle.

2. How do I find the measure of HG in a geometry problem?

To find the measure of HG, you can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. You can also use trigonometric ratios such as sine, cosine, and tangent to find the measure of HG.

3. What does the X-axis angle represent in a geometry problem?

The X-axis angle represents the angle formed by the hypotenuse and the X-axis, which is the horizontal line on a coordinate plane. It is usually measured in degrees and can be used to determine the position of a point on a coordinate plane.

4. How do I find the measure of the X-axis angle in a geometry problem?

To find the measure of the X-axis angle, you can use inverse trigonometric functions such as inverse sine, inverse cosine, and inverse tangent. These functions will give you the angle measure when given the ratio of the sides of a right triangle.

5. Can I use any other methods to find the measure of HG and the X-axis angle?

Yes, there are other methods that can be used to find the measure of HG and the X-axis angle, such as the Law of Sines and the Law of Cosines. These methods can be useful when the given information is not a right triangle or when you have more than one angle and side measure.

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