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Trigonometry Applications Worksheet and Solutions

Hints on solving trigonometry applications or problems:

  • If no diagram is given, draw one yourself.
  • Mark the right angles in the diagram.
  • Show the sizes of the other angles and the lengths of any lines that are known
  • Mark the angles or sides you have to calculate.
  • Consider whether you need to create right triangles by drawing extra lines. For example, divide an isosceles triangle into two congruent right triangles.
  • Decide whether you will need Pythagoras theorem, sine, cosine or tangent.
  • Check that your answer is reasonable. The hypotenuse is the longest side in a right triangle.

Refer to the lesson on how to solve trigonometry applications for more information and examples.

Fill in all the gaps, then press "Check" to check your answers. Use the "Hint" button to get a free letter if an answer is giving you trouble. You can also click on the "[?]" button to get a clue. Note that you will lose points if you ask for hints or clues!

Solve the following.

Give your answer to the nearest tenths.

What is the angle of elevation of the top of a tree 12.7 m from a point 23.7 m away on level ground?

An isosceles triangle has a vertical angle of 108 and a base 20 cm long. Calculate its altitude.

An aerial mast is supported by four wires attached to points on the ground each 57 m away from the foot of the mast. If each wire makes an angle of 32 with the horizontal, find the height of the mast.

To find the width of a river, a boy places a wooden peg at a point A on one side directly opposite an object B on the opposite bank. From A, he walks 50 m along the bank to a point C. He observes that angle ACB is 34. Calculate the width of the river.

The angle of elevation of the top of a post from a point on level ground 38 m away is 33.23. Find the height of the post.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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