# Exercises: Sine, Cosine and Tangent Ratios and Applications of Trigonometry (6.5)

**Exercises: Label Sides of Triangles**

Instructions: For questions 1-2, label the sides of the triangle.

**1.**

**Solution**

**2.**

**Exercises: Finding Adjacent or Opposite Sides**

Instructions: For questions 3-4, solve.

**3. If the reference angle in Question 1 is B, Find the adjacent?**

**Solution**

c

**4. If the reference angle in Question 2 is Z, find the opposite?**

**Exercises: Label and Find Sides of a Triangle**

Instructions: For questions 5-6, label the sides of the triangle and find the hypotenuse, opposite and adjacent.

**5.**

**Solution**

g is opposite , f is adjacent, and e is hypotenuse

**6.**

**Exercises: Find the Given Ratios**

Instructions: For questions 7-10, use your calculator to find the given ratios. Round to four decimal places if necessary.

**7. [latex]\sin {47}^{\circ}[/latex]**

**Solution**

[latex]0.7314[/latex]

**8. [latex]\cos {82}^{\circ}[/latex]**

**9. [latex]\tan {12}^{\circ}[/latex]**

**Solution**

[latex]0.2126[/latex]

**10. [latex]\sin {30}^{\circ}[/latex]**

**Exercises: Find the Sine, Cosine, and Tangent of [latex]{\color{White}{\theta}}[/latex]**

Instructions: For the given triangles in questions 11-14, find the sine, cosine and tangent of the [latex]\theta[/latex].

**11.**

**Solution**

[latex]\text{sin }\theta=\frac{g}{e},\;\text{cos }\theta=\frac{f}{e},\;\text{tan }\theta=\frac{g}{f}[/latex]

**12.**

**13.**

**Solution**

[latex]\text{sin }\theta=\frac{s}{r},\;\text{cos }\theta=\frac{t}{r},\;\text{tan }\theta=\frac{s}{t}[/latex]

**14.**

**Exercises: Find the Missing Side**

Instructions: For the given triangles in questions 15-18, find the missing side. Round it to one decimal place.

**15. Find the hypotenuse.**

**Solution**

[latex]b=19.8[/latex]

**16. Find [latex]b[/latex] if [latex]a=6[/latex].**

**17. Find the opposite.**

**Solution**

[latex]c=12[/latex]

**18. Find the adjacent.**

**Exercises: Find the Missing Sides**

Instructions: For the given triangles in questions 19-20, find the missing sides. Round it to one decimal place.

**19.**

**Solution**

[latex]y=19.3,\;z=8.2[/latex]

**20.**

**Exercises: Solve Triangles**

Instructions: For questions 21-24, solve the triangles. Round to one decimal place.

**21.**

**Solution**

[latex]\angle B=61^\circ,\;\angle C= 29^\circ,\;\angle D=90^\circ,\;b=38.5,\;c=21.3,\;d=44[/latex]

**22.**

**23.**

**Solution**

[latex]\angle T=36.9^\circ,\;\angle R=90^\circ,\;\angle S=53.1^\circ,\;t=15,\;r=25,\;s=20[/latex]

**24.**

**Exercises: Word Problems**

Instructions: For questions 25-30, answer the given word problems.

**25. Kim stands [latex]75[/latex] metres from the bottom of a tree and looks up at the top of the tree at a [latex]48^\circ[/latex] angle. How tall is the tree?**

**Solution**

[latex]83.3[/latex] m

**26. A tree makes a shadow that is [latex]6[/latex] metres long when the angle of elevation to the sun is [latex]52^\circ[/latex]. How tall is the tree?**

**27. A ladder that is [latex]15[/latex] feet is leaning against a house and makes a [latex]45^\circ[/latex] angle with the ground. How far is the base of the ladder from the house?**

**Solution**

[latex]10.6[/latex] ft

**28. Roxanne is flying a kite and has let out [latex]100[/latex] feet of string. The angle of elevation with the ground is [latex]38^\circ[/latex]. How high is her kite above the ground?**

**29. Marta is flying a kite and has let out [latex]28[/latex] metres of string. If the kite is [latex]10[/latex] metres above the ground, what is the angle of elevation?**

**Solution**

[latex]20.9^\circ[/latex]

**30. An airplane takes off from the ground at the angle of [latex]25^\circ[/latex]. If the airplane traveled [latex]200[/latex] kilometres, how high above the ground is it?**