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7.2E: Right Triangle Trigonometry (Exercises)

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    For the following exercises, use side lengths to evaluate.

    17. \(\cos \frac{\pi}{4}\)

    18. \(\cot \frac{\pi}{3}\)

    19. \(\tan \frac{\pi}{6}\)

    20. \(\cos \left(\frac{\pi}{2}\right)=\sin \left(\longrightarrow^{\circ}\right)\)

    21. \(\csc \left(18^{\circ}\right)=\sec \left(\longrightarrow^{\circ}\right)\)

    For the following exercises, use the given information to find the lengths of the other two sides of the right triangle.

    22. \(\cos B=\frac{3}{5}, a=6\)

    23. \(\tan A=\frac{5}{9}, b=6\)

    For the following exercises, use Figure 1 to evaluate each trigonometric function.

    A right triangle with side lengths of 11 and 6. Corners A and B are also labeled.  The angle A is opposite the side labeled 11.  The angle B is opposite the side labeled 6.

    Figure 1

    24. \(\sin A\)

    25. \(\tan B\)

    For the following exercises, solve for the unknown sides of the given triangle.


    A right triangle with corners labeled A, B, and C. Hypotenuse has length of 4 times square root of 2. Other angles measure 45 degrees.


    A right triangle with hypotenuse with length 5, and an angle of 30 degrees.

    28. A 15-ft ladder leans against a building so that the angle between the ground and the ladder is \(70^{\circ} .\) How high does the ladder reach up the side of the building? Find the answer to four decimal places.

    29. The angle of elevation to the top of a building in Baltimore is found to be 4 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building. Find the answer to four decimal places.

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