# 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. Figure 1

24. $$\sin A$$

25. $$\tan B$$

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

26. 27. 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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