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How to Determine the Height of a Tree

You can use a trigonometry function to find the height of a tree while standing on the ground. For example, suppose you’re flying a kite, and it gets caught at the top of a tree. You’ve let out all 100 feet of string for the kite, and the angle that the string makes with the ground (the angle of elevation) is 75 degrees. Instead of worrying about how to get your kite back, you wonder, “How tall is that tree?”


The preceding figure shows the scenario. To find a solution to your quandary, follow these steps:

  1. Identify the parts of the right triangle that you can use to solve the problem.

    The hypotenuse of the right triangle is the length of the string. The side opposite the 75-degree angle is what you’re solving for; call it x.

  2. Determine which trig function to use.

    The hypotenuse and opposite side are each parts of the sine ratio.

  3. Write an equation with the trig function, and then input the values that you know.

    The 75-degree angle isn’t one of the more-common angles, so use a scientific calculator to obtain a value for the sine, correct to three decimal places.

  4. Solve the equation.

    Cross-multiplying, you get


    The tree is almost 97 feet tall.

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