# Module 31: Right Triangle Trigonometry

**You may use a calculator throughout this module.**

*Sine, Cosine, Tangent*

- The
*sine*of the angle is the ratio of the opposite side to the hypotenuse. - The
*cosine*of the angle is the ratio of the adjacent side to the hypotenuse. - The
*tangent*of the angle is the ratio of the opposite side to the adjacent side.

**SOHCAHTOA**

Exercises

**1.**

**2.**

Exercises

**3.**sin

**4.**cos

**5.**tan

**6.**sin

**7.**cos

**8.**tan

Exercises

**9.**sin

**10.**cos

**11.**tan

**12.**sin

**13.**cos

**14.**tan

*Trigonometry Applications*

Exercises

**15.**

**16.**

**17.**

**18.**

**19.**

**20.**

**21.** A guy wire is attached to a utility pole. The wire is anchored to the ground 15 feet from the base of the pole, forming a angle with the level ground. What is the length of the wire, to the nearest foot?

**22.** A 19-foot ladder is leaning against a wall, forming a angle with the level ground. What is the vertical height of the place where the ladder contacts the wall?

**23.** During intermission of a hockey game, one lucky fan gets to shoot a puck from center ice at the goal, 90 feet away, for the chance to win a truck. Actually, there is a sheet of plywood blocking the entire goal except for a 6-inch wide hole in the bottom center. If the fan shoots the puck hard enough, aiming directly at the center of the hole, they win, of course. If their aim is off by , will they still win the truck? (If it helps, a hockey puck is 3 inches in diameter.)

*Inverse Sine, Inverse Cosine, Inverse Tangent*

Exercises

**24.**

**25.**

**26.**

*Inverse Trigonometry Applications*

Exercises

**27.**

**28.**

**29.**

**30.**

**31.**

**32.**

**33.** The entrance to a public building is 2 feet higher than the courtyard in front of the entrance. A ramp is being constructed, continuous with no switchbacks or level platforms, with a surface length of 25 feet. ADA regulations limit the angle of elevation to a maximum of approximately .^{[1]} Does the ramp’s design meet ADA standards?

**34.** A rule of thumb for ladder safety is that the vertical height where the ladder touches the wall should be four times the horizontal distance from the base of the ladder to the wall.^{[2]} To the nearest degree, what is the angle between the ladder and the floor in this scenario?

*Using Multiple Methods*

Exercises

**35. ** First, use inverse tangent to determine the value of . Round to the nearest whole degree.

**36. ** Next, use sine with to determine the value of . Round to the nearest tenth.

**37. ** Next, use cosine with to determine the value of . Round to the nearest tenth.

**38.** Finally, use the Pythagorean Theorem to determine the value of . Round to the nearest tenth.

**39.** Compare your answers for Exercises 36-38. Why are they different?

- This is implied at https://www.ada-compliance.com/ada-compliance/ada-ramp but not directly stated. We'll verify this angle measure in the next module. ↵
- https://www.americanladderinstitute.org/page/Ladders101 ↵