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.

26.

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

27.

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

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.