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Chapter 2: Trigonometric Ratios

Exercises: Chapter 2 Review Problems

Chapter Review Suggested Problems

Problems: # 10, 14, 18, 22, 22, 24, 26, 40

 

Exercises for Chapter 2 Review

Exercise Group

For Problems 1–6, explain why the description of [latex]\triangle ABC[/latex] is impossible.

1.

[latex]A \lt B \lt C{,}[/latex] and [latex]B = 93°[/latex]

2.

[latex]A \lt B \lt C{,}[/latex] and [latex]C = 58°[/latex]

Exercise Group

For Problems 7 and 8, sketch the triangle.

7.

The three angles of a triangle are [latex]20°, 50°, {and}~ 110°,[/latex] and the three sides are [latex]15[/latex] cm, [latex]6.7[/latex] cm, and [latex]18.4[/latex] cm. Sketch and label the triangle.

8.

Sketch and label an isosceles triangle with sides [latex]5[/latex] in and [latex]12[/latex] in, and one angle [latex]78°{.}[/latex]

Exercise Group

For Problems 9–12, find the unknown side of the right triangle.

9.

right triangle with sides 72 and 65

10.

right triangle with sides 88 and 105

11.

right triangle with hyp 65 and side 39

12.

right triangle with hyp 175 and side 168

13.

A triangle has sides of length [latex]33, 56,[/latex] and [latex]65[/latex]. Is it a right triangle?

Exercise Group

For Problems 19–22,

  1. Find the unknown side.
  2. Find the sine, cosine, and tangent of [latex]\theta{.}[/latex] Round your answers to four decimal places.
19.

right triangle with sides 54 and 67

20.

right triangle with sides 4.4 and 3.2

21.

right triangle with hyp 23 and side 16

22.

right triangle with hyp 38 and side 29

Exercise Group

For Problems 23–28, find the unknown side of the triangle. Round your answer to hundredths.

23.

right triangle with hyp 27 and angle 73

24.

right triangle with hyp 36 and angle 51

25.

right triangle with side 7 adjacent to angle 27

26.

right triangle with side 2 opposite angle 38

27.

right triangle with side 87 opposite angle 29

28.

right triangle with hyp 10 and angle 47

Exercise Group

For Problems 29–32, solve the triangle. Give exact values.

29.

right triangle with side 23 opposite angle 60

30.

right triangle with hyp 14 and angle 45

31.

triangle with angles 30 and 45 and height 10

32.

triangle with angles 45 and 60 and height 12

33.

Find the diameter of a hex nut if one of the sides is 1.5 cm.

hexagon

 

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