Things You'll Need:
- Scientific calculator
- Paper
- Pencil
- Formulas
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Step 1
Right triangleIdentify the hypotenuse in a right triangle by looking for the longest side that is located opposite the 90-degree angle. Once you have located the hypotenuse, you can identify the adjacent leg because it meets the hypotenuse at angle A. The opposite side remains, located opposite to angle A, and it is also perpendicular to the base. Perpendicular means that it sticks straight up from the 90-degree angle.
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Step 2
Use the Pythagorean Theorem a2 + b2 = c2 to identify the length of a side when two of the sides are known. “The square of the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides.” Look at the right triangle in step 1. If c is the hypotenuse and we do not know the length, but we know a=5 and b=7. Then we need to find the square of 5. That is 5 times 5 or 25 and the square of 7, which is 7 times 7 or 49. Now add these two numbers together, 25 plus 49 equals 74. Now we know that 74 is the square of the hypotenuse. To locate the actual length of they hypotenuse we would find the square root of 74, which equals 8.60233.
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Step 3
Find the coordinates of a ship.Use these formulas to find the coordinates and distance to a ship if you are in navigation or to a property line if you are a surveyor.
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Step 4
A surveyor locating coordinatesThink triangulation, if you know the length of one side of the triangle and two of the interior angles, or two sides and one interior angle, then you can use the law of sines to find missing information or needed coordinates. Remember that according to the law of sines, the ratio of the side of a triangle to the opposite angle is the same for each side and each opposite angle of the triangle.
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Step 5
Remember the triangle we used in the Pythagorean Theorem example. We know the sides a=5 and b=7 and c=8.60233 and C a right angle so it equals 90 degrees. We know that all the interior angles of a triangle equal 180 and since angle C=90 we know that Angle A + Angle B=90 because 90+90=180.
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Step 6
Write down your equation for the law of sines now that you have this information. sin A/5=sin B/7=sin 90/8.60233. Now you will use cross multiplication to figure out A and C, sin B/7=sin 90/8.60233. 90x7=630 and 8.60233B, therefore, B=630/8.60233, therefore, B=73.23597 degrees. We can add B to C or 73.23597+90=163.23597 and subtract that answer from 180 degrees to find angle a. 180-163.23597=16.76403. We now know all three angles A=16.76403 degrees, B=73.23597 degrees, and C=90 degrees. We could use this information to place the corner post on a person's land identifying their boundaries.
