Chapter 2: Trigonometric Ratios
Exercises: 2.3 Solving Right Triangles
Skills
Suggested Homework Problems
Exercises Homework 2.3
Exercise Group
For Problems 1–4, solve the triangle. Round answers to hundredths.
2.
3.
4.
Exercise Group
For Problems 5–10,
- Sketch the right triangle described.
- Solve the triangle.
5.
[latex]A = 42{^o}, c = 26[/latex]
6.
[latex]B = 28{^o}, c = 6.8[/latex]
7.
[latex]B = 33{^o}, a = 300[/latex]
8.
[latex]B = 79{^o}, a = 116[/latex]
9.
[latex]A = 12{^o}, a = 4[/latex]
10.
[latex]A = 50{^o}, a = 10[/latex]
Exercise Group
For Problems 11–16,
- Sketch the right triangle described.
- Without doing the calculations, list the steps you would use to solve the triangle.
11.
[latex]B = 53.7{^o}, b = 8.2[/latex]
12.
[latex]B = 80{^o}, a = 250[/latex]
13.
[latex]A = 25{^o}, b = 40[/latex]
14.
[latex]A = 15{^o}, c = 62[/latex]
15.
[latex]A = 64.5{^o}, c = 24[/latex]
16.
[latex]B = 44{^o}, b = 0.6[/latex]
Exercise Group
For Problems 17–22, find the labeled angle. Round your answer to tenths of a degree.
17.
18.
19.
20.
21.
22.
Exercise Group
For Problems 23–28, evaluate the expression and sketch a right triangle to illustrate.
23.
[latex]\sin^{-1} 0.2[/latex]
24.
[latex]\cos^{-1} 0.8[/latex]
25.
[latex]\tan^{-1} 1.5[/latex]
26.
[latex]\tan^{-1} 2.5[/latex]
27.
[latex]\cos^{-1} 0.2839[/latex]
28.
[latex]\sin^{-1} 0.4127[/latex]
Exercise Group
For Problems 29–32, write two different equations for the statement.
29.
The cosine of [latex]15 {^o}[/latex] is [latex]0.9659\text{.}[/latex]
30.
The sine of [latex]70 {^o}[/latex] is [latex]0.9397\text{.}[/latex]
31.
The angle whose tangent is [latex]3.1445[/latex] is [latex]65 {^o}\text{.}[/latex]
32.
The angle whose cosine is [latex]0.0872[/latex] is [latex]85 {^o}\text{.}[/latex]
33.
Evaluate the expressions and explain what each means.
[latex]\begin{equation*} \sin^{-1} (0.6), (\sin 6{^o})^{-1} \end{equation*}[/latex]
34.
Evaluate the expressions and explain what each means.
[latex]\begin{equation*} \cos^{-1} (0.36), (\cos 36{^o})^{-1} \end{equation*}[/latex]
Exercise Group
For Problems 35–38,
- Sketch a right triangle that illustrates the situation. Label your sketch with the given information.
- Choose the appropriate trig ratio and write an equation, then solve the problem.
35.
The gondola cable for the ski lift at Snowy Peak is [latex]2458[/latex] yards long and climbs [latex]1860[/latex] feet. What angle with the horizontal does the cable make?
36.
The Leaning Tower of Pisa is [latex]55[/latex] meters in length. An object dropped from the top of the tower lands [latex]4.8[/latex] meters from the base of the tower. At what angle from the horizontal does the tower lean?
37.
A mining company locates a vein of minerals at a depth of [latex]32[/latex] meters. However, there is a layer of granite directly above the minerals, so they decide to drill at an angle, starting [latex]10[/latex] meters from their original location. At what angle from the horizontal should they drill?
38.
The bird