Exercises: 2.2 Right Triangle Trigonometry
Exercises Homework 2.2
Skills
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- Use measurements to calculate the trigonometric ratios for acute angles #1-10, 57-60
- Use trigonometric ratios to find unknown sides of right triangles #11-26
- Solve problems using trigonometric ratios #27-34, 41-46
- Use trig ratios to write equations relating the sides of a right triangle #35-40
- Use relationships among the trigonometric ratios #47-56, 61-68
Problems: 6, 10, 58, 12, 22, 30, 42, 46, 38, 40, 50, 62.
1.
Here are two right triangles with a [latex]65 °[/latex] angle.
- Measure the sides [latex]AB[/latex] and [latex]BC[/latex] with a ruler. Use the lengths to estimate [latex]\sin 65°{.}[/latex]
- Measure the sides [latex]AD[/latex] and [latex]DE[/latex] with a ruler. Use the lengths to estimate [latex]\sin 65°{.}[/latex]
- Use your calculator to look up [latex]\sin 65°{.}[/latex] Compare your answers. How close were your estimates?
2.
Use the figure in Problem 1 to calculate two estimates each for the cosine and tangent of [latex]65 °{.}[/latex] Compare your estimates to your calculator’s values for [latex]\cos 65°[/latex] and [latex]\tan 65°{.}[/latex]
3.
Here are two right triangles with a [latex]40 °[/latex] angle.
- Measure the sides [latex]AB[/latex] and [latex]AC[/latex] with a ruler. Use the lengths to estimate [latex]\cos 40°{.}[/latex]
- Measure the sides [latex]AD[/latex] and [latex]AE[/latex] with a ruler. How close were your estimates?
4.
Use the figure in Problem 2 to calculate two estimates each for the cosine and tangent of [latex]40 °{.}[/latex] Compare your estimates to your calculator’s values for [latex]\sin 40°[/latex] and [latex]\tan 40°{.}[/latex]
Exercise Group
For the right triangles in Problems 5–10,
- Find the length of the unknown side.
- Find the sine, cosine, and tangent of [latex]\theta \text{.}[/latex] Round your answers to four decimal places.
5.
6.
7.
8.
9.
10.
Exercise Group
For Problems 11–16,
- Sketch and label the sides of a right triangle with angle [latex]\theta\text{.}[/latex]
- Sketch and label another right triangle with angle [latex]\theta[/latex] and longer sides.
11.
[latex]\cos \theta = \dfrac{3}{5}[/latex]
12.
[latex]\tan \theta = \dfrac{7}{2}[/latex]
13.
[latex]\tan \theta = \dfrac{11}{4}[/latex]
14.
[latex]\sin \theta = \dfrac{4}{9}[/latex]
15.
[latex]\sin \theta = \dfrac{1}{9}[/latex]
16.
[latex]\cos \theta = \dfrac{7}{8}[/latex]
Exercise Group
For Problems 17–22, use one of the three trigonometric ratios to find the unknown side of the triangle. Round your answer to hundredths.
17.
18.
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20.
21.
22.
Exercise Group
For Problems 23–26, sketch and label a right triangle with the given properties.
23.
One angle is [latex]40°{,}[/latex] the side opposite that angle is 8 inches
24.
One angle is [latex]65°{,}[/latex] the side adjacent to that angle is 30 yards
25.
One angle is [latex]28°{,}[/latex] the hypotenuse is 56 feet
26.
One leg is [latex]15[/latex] meters, the hypotenuse is [latex]18[/latex] meters
Ex