# 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. $\sin {47}^{\circ}$
Solution

$0.7314$

8. $\cos {82}^{\circ}$

9. $\tan {12}^{\circ}$
Solution

$0.2126$

10. $\sin {30}^{\circ}$

## Exercises: Find the Sine, Cosine, and Tangent of ${\color{White}{\theta}}$

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

11.

Solution

$\text{sin }\theta=\frac{g}{e},\;\text{cos }\theta=\frac{f}{e},\;\text{tan }\theta=\frac{g}{f}$

12.

13.

Solution

$\text{sin }\theta=\frac{s}{r},\;\text{cos }\theta=\frac{t}{r},\;\text{tan }\theta=\frac{s}{t}$

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

$b=19.8$

16. Find $b$ if $a=6$.

17. Find the opposite.

Solution

$c=12$

## 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

$y=19.3,\;z=8.2$

20.

## Exercises: Solve Triangles

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

21.

Solution

$\angle B=61^\circ,\;\angle C= 29^\circ,\;\angle D=90^\circ,\;b=38.5,\;c=21.3,\;d=44$

22.

23.

Solution

$\angle T=36.9^\circ,\;\angle R=90^\circ,\;\angle S=53.1^\circ,\;t=15,\;r=25,\;s=20$

24.

## Exercises: Word Problems

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

25. Kim stands $75$ metres from the bottom of a tree and looks up at the top of the tree at a $48^\circ$ angle. How tall is the tree?
Solution

$83.3$ m

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

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

$10.6$ ft

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

29. Marta is flying a kite and has let out $28$ metres of string. If the kite is $10$ metres above the ground, what is the angle of elevation?
Solution

$20.9^\circ$

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