How to Find a Triangle Measurement on a Circle With a Tangent
Trig is not the shorthand name of Roy Roger's horse. The full word is trigonometry, and this branch of mathematics involves the measurements of triangles and circles. Many students frustrate themselves by making the problems far too difficult. When you have a tangent to go by, finding a triangle measurement is fairly simple.
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Instructions
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Make sure your assignment has no special instructions, such as "do not write on this page," "write your answers on a separate sheet of paper," or "show your work." With this cleared up, look at the problem itself.
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Look at where the tangent touches the outside of the circle. It will do this in only one place. The circle's radius will lead from that point to the exact center of the circle at a 90 degree angle. Draw a line between the two with a ruler.
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Put a point at the circle's center named "A". Place another point "B" where the tangent meets the outside edge of the circle. Use a ruler to draw a straight line vertically from B toward the top of the paper and from A to the vertical line. Where they intersect, draw a point and label it "C". Mark your 90 degree angle at B.
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Use the Pythagorean theorem for any triangles with two values given to the line segments a, b, and c.
Example: a^2 + b^2 = c^2, where a = 2 and b = 5.
(2)^2 + (5)^2 = c^2
4 + 25 = c^2
29 = c^2
Take the square root of both sides to cancel out the square.
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You can also use tan A = sin A / cos A: the opposite side divided by the adjacent side. Small letters are line segments.
Example: In right triangle ABC, a = 35 feet and tan A = 5. Find b and c.
We have the tangent A (2), and the opposite (a, 35 feet).
tan A = opposite / adjacent (or a/b)
2 = 35 / b
2b = 35
b = 35 / 2, or 17.5 feet
Use the Pythagorean theorem to solve for c. (35)^2 + (17.5)^2 = c^2
The answer for c, rounded, should be 39.13 feet.
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Tips & Warnings
Write out your formulas on the page, or somewhere close by, so that you can refer to them easily.
Write out what is given to you in the problem itself, so that you can correctly fill in the appropriate slots in your formulas.
Use a calculator when finding the square root or squares of larger numbers to save room.
Remember that ABC is used for the points of the triangle, while abc is used for the line segments. Line segments may also be written out as AB with a line over them.
Don't forget to add "feet," "yards," "inches," or any other measurement to your final answers.
References
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