Q. I need help finding the two acute angles of a right triangle. Well actually i need the formula. I'm having trouble tracking it down on the webz. I know the length of the 3 sides and just need to find the angles. It has something to do with arctangent i think. I'm bad at math. Anyway any help would be awesome.
A. SOHCAHTOA
Sin = Opposite / Hypotoneuse
Cosine = Adjacent / Hypotoneuse
Tangent = Opposite / Adjacent
So if you pick the angle you want, take the length OPPOSITE the angle and the length ADJACENT to the angle, divide the opposite by the adjacent that gives you the ratio. Then take the ark tan of that ratio that will give you the angle.
Since it's a right angled triangle one of the other angles must be 90 degrees.
The remaining angle will be 90 degrees - the angle you calculated.
If you only had two sides and not the third you could use the arc sin or arc cos or arc tan depending on which two lengths you knew and which angle you wanted to find.
Sin = Opposite / Hypotoneuse
Cosine = Adjacent / Hypotoneuse
Tangent = Opposite / Adjacent
So if you pick the angle you want, take the length OPPOSITE the angle and the length ADJACENT to the angle, divide the opposite by the adjacent that gives you the ratio. Then take the ark tan of that ratio that will give you the angle.
Since it's a right angled triangle one of the other angles must be 90 degrees.
The remaining angle will be 90 degrees - the angle you calculated.
If you only had two sides and not the third you could use the arc sin or arc cos or arc tan depending on which two lengths you knew and which angle you wanted to find.
What are tips for solving angles in circles that are inscribed or central angles?
Q. Basically, I just need tips for solving angles in circles that are inscribed or central angles (yes, bad wording.) I just kinda miss the "big" picture sometimes. I get the concepts of the theorems, but actually finding the angles is a pretty big challenge for me sometimes.
A. You can go on:
http://www.mathwarehouse.com/geometry/circle/inscribed-angle.html
Here are my tips that I use:
Formula for inscribed angle
If you know the length of the minor arc and radius, the inscribed angle is:
where:
L is the length of the minor (shortest) arc AB
R is the radius of the circle
Ï is Pi, approximately 3.142
Arcs and Chords
The two points A and B can be isolated points, or they could be the end points of an arc or chord. When they are the end points of an arc, the angle is sometimes called the peripheral angle of the arc.
Central Angle
A similar concept is the central angle. This is the angle subtended at the center of the circle by the two given points.
The central angle is always twice the inscribed angle. Relationship to Thales' Theorem
Refer to the above figure. If the two points A,B form a diameter of the circle, the inscribed angle will be 90°, which is Thales' Theorem. You can verify this yourself by solving the formula above using an arc length of half the circumference of the circle.
You can also move the points A or B above until the inscribed angle is exactly 90°. You will see that the points A and B are then diametrically opposite each other.
Hope I helped!
http://www.mathwarehouse.com/geometry/circle/inscribed-angle.html
Here are my tips that I use:
Formula for inscribed angle
If you know the length of the minor arc and radius, the inscribed angle is:
where:
L is the length of the minor (shortest) arc AB
R is the radius of the circle
Ï is Pi, approximately 3.142
Arcs and Chords
The two points A and B can be isolated points, or they could be the end points of an arc or chord. When they are the end points of an arc, the angle is sometimes called the peripheral angle of the arc.
Central Angle
A similar concept is the central angle. This is the angle subtended at the center of the circle by the two given points.
The central angle is always twice the inscribed angle. Relationship to Thales' Theorem
Refer to the above figure. If the two points A,B form a diameter of the circle, the inscribed angle will be 90°, which is Thales' Theorem. You can verify this yourself by solving the formula above using an arc length of half the circumference of the circle.
You can also move the points A or B above until the inscribed angle is exactly 90°. You will see that the points A and B are then diametrically opposite each other.
Hope I helped!
Geometry - How to find an interior angle in a circle?
Q. On my homework there is a diagram of a circle with and angle inside coming off the center of the circle. The arc of that angle is 96 degrees. How would I find the angle measurement?
A. if the angle is in radians, and the radius is 1 unit then the subtended arc IS the same as the central angle (in radians )
.......96° is an unusual way to measure an arc length..its usually a length, like 3.4 units..... but that means the central angle is also 96°
.......96° is an unusual way to measure an arc length..its usually a length, like 3.4 units..... but that means the central angle is also 96°
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