How To Solve Trigonometric Problems

The angle measured to the top of the lighthouse is 65°. We also know the angle to the base of the measuring stick is 2°.

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Two trigonometric ratios use the Two surveyors measure the length of the field.

One surveyor stands at one end of the field with the measuring equipment, the other surveyor stands at the other end of the field with a measuring stick 2 m high.

However, we know that the ratio of the unknown length to the known length (i.e.

shadow) must be the same as for the Potiphar-triangle: Thales of Miletus measures the length of the shadow cast by the great pyramid and discovers that it is 17 m to the base of the pyramid.

Step 4: Mark the angles or sides you have to calculate.

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Step 3: Show the sizes of the other angles and the lengths of any lines that are known.

The tree and its shadow form another right angle triangle.

The rays of the sun (which are invisible) form the hypotenuse of these right angle triangles.

We know that the sum of the two opposite sides must be 2 m.

We also know the angles for both right angle triangles, so we know the ratios the sides have: From trigonometric definitions we know that It does not matter which of the lengths we use (as long as we use them in the right place), the answer will still be the same (any small differences in the answers are due to rounding errors – you can avoid / minimize these by using the full precision provided by your calculator.

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