{"id":13857,"date":"2018-06-14T23:52:45","date_gmt":"2018-06-14T23:52:45","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/chapter\/solutions-15\/"},"modified":"2021-11-22T22:01:00","modified_gmt":"2021-11-22T22:01:00","slug":"solutions-right-triangle-trig","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/solutions-right-triangle-trig\/","title":{"raw":"Solutions: Right Triangle Trigonometry","rendered":"Solutions: Right Triangle Trigonometry"},"content":{"raw":"

Solutions to Try Its<\/h2>\r\n1.\u00a0[latex]\\frac{7}{25}[\/latex]\r\n\r\n2.\u00a0[latex]\\begin{array}{l}sin t=\\frac{33}{65},\\cos t=\\frac{56}{65},tan t=\\frac{33}{56},\\hfill \\\\ \\sec t=\\frac{65}{56},\\csc t=\\frac{65}{33},\\cot t=\\frac{56}{33}\\hfill \\end{array}[\/latex]\r\n\r\n3.\u00a0[latex]\\sin \\left(\\frac{\\pi }{4}\\right)=\\frac{\\sqrt{2}}{2},\\cos \\left(\\frac{\\pi }{4}\\right)=\\frac{\\sqrt{2}}{2},\\tan \\left(\\frac{\\pi }{4}\\right)=1[\/latex],\r\n[latex]\\sec \\left(\\frac{\\pi }{4}\\right)=\\sqrt{2},csc\\left(\\frac{\\pi }{4}\\right)=\\sqrt{2},\\cot \\left(\\frac{\\pi }{4}\\right)=1[\/latex]\r\n\r\n4. 2\r\n\r\n5.\u00a0[latex]\\text{adjacent}=10[\/latex]; [latex]\\text{opposite}=10\\sqrt{3}[\/latex] ; missing angle is [latex]\\frac{\\pi }{6}[\/latex]\r\n\r\n6.\u00a0About 52 ft\r\n

Solutions to Odd-Numbered Exercises<\/h2>\r\n1.\r\n\"A\r\n\r\n3. The tangent of an angle is the ratio of the opposite side to the adjacent side.\r\n\r\n5.\u00a0For example, the sine of an angle is equal to the cosine of its complement; the cosine of an angle is equal to the sine of its complement.\r\n\r\n7.\u00a0[latex]\\frac{\\pi }{6}[\/latex]\r\n\r\n9.\u00a0[latex]\\frac{\\pi }{4}[\/latex]\r\n\r\n11.\u00a0[latex]b=\\frac{20\\sqrt{3}}{3},c=\\frac{40\\sqrt{3}}{3}[\/latex]\r\n\r\n13.\u00a0[latex]a=10,000,c=10,000.5[\/latex]\r\n\r\n15.\u00a0[latex]b=\\frac{5\\sqrt{3}}{3},c=\\frac{10\\sqrt{3}}{3}[\/latex]\r\n\r\n17.\u00a0[latex]\\frac{5\\sqrt{29}}{29}[\/latex]\r\n\r\n19.\u00a0[latex]\\frac{5}{2}[\/latex]\r\n\r\n21.\u00a0[latex]\\frac{\\sqrt{29}}{2}[\/latex]\r\n\r\n23.\u00a0[latex]\\frac{5\\sqrt{41}}{41}[\/latex]\r\n\r\n25.\u00a0[latex]\\frac{5}{4}[\/latex]\r\n\r\n27.\u00a0[latex]\\frac{\\sqrt{41}}{4}[\/latex]\r\n\r\n29.\u00a0[latex]c=14, b=7\\sqrt{3}[\/latex]\r\n\r\n31.\u00a0[latex]a=15, b=15[\/latex]\r\n\r\n33.\u00a0[latex]b=9.9970, c=12.2041[\/latex]\r\n\r\n35.\u00a0[latex]a=2.0838, b=11.8177[\/latex]\r\n\r\n37.\u00a0[latex]a=55.9808,c=57.9555[\/latex]\r\n\r\n39.\u00a0[latex]a=46.6790,b=17.9184[\/latex]\r\n\r\n41.\u00a0[latex]a=16.4662,c=16.8341[\/latex]\r\n\r\n43.\u00a0188.3159\r\n\r\n45.\u00a0200.6737\r\n\r\n47.\u00a0498.3471 ft\r\n\r\n49.\u00a01060.09 ft\r\n\r\n51.\u00a027.372 ft\r\n\r\n53.\u00a022.6506 ft\r\n\r\n55.\u00a0368.7633 ft\r\n\r\n56.\u00a0[latex]{7.2}^{\\circ }[\/latex]\r\n\r\n58.\u00a0[latex]{5.7}^{\\circ }[\/latex]\r\n\r\n60.\u00a0[latex]{82.4}^{\\circ }[\/latex]\r\n\r\n62.\u00a0[latex]{31.0}^{\\circ }[\/latex]\r\n\r\n64.\u00a0[latex]{88.7}^{\\circ }[\/latex]\r\n\r\n66.\u00a0[latex]{59.0}^{\\circ }[\/latex]\r\n\r\n68.\u00a0[latex]{36.9}^{\\circ }[\/latex]","rendered":"

Solutions to Try Its<\/h2>\n

1.\u00a0[latex]\\frac{7}{25}[\/latex]<\/p>\n

2.\u00a0[latex]\\begin{array}{l}sin t=\\frac{33}{65},\\cos t=\\frac{56}{65},tan t=\\frac{33}{56},\\hfill \\\\ \\sec t=\\frac{65}{56},\\csc t=\\frac{65}{33},\\cot t=\\frac{56}{33}\\hfill \\end{array}[\/latex]<\/p>\n

3.\u00a0[latex]\\sin \\left(\\frac{\\pi }{4}\\right)=\\frac{\\sqrt{2}}{2},\\cos \\left(\\frac{\\pi }{4}\\right)=\\frac{\\sqrt{2}}{2},\\tan \\left(\\frac{\\pi }{4}\\right)=1[\/latex],
\n[latex]\\sec \\left(\\frac{\\pi }{4}\\right)=\\sqrt{2},csc\\left(\\frac{\\pi }{4}\\right)=\\sqrt{2},\\cot \\left(\\frac{\\pi }{4}\\right)=1[\/latex]<\/p>\n

4. 2<\/p>\n

5.\u00a0[latex]\\text{adjacent}=10[\/latex]; [latex]\\text{opposite}=10\\sqrt{3}[\/latex] ; missing angle is [latex]\\frac{\\pi }{6}[\/latex]<\/p>\n

6.\u00a0About 52 ft<\/p>\n

Solutions to Odd-Numbered Exercises<\/h2>\n

1.
\n\"A<\/p>\n

3. The tangent of an angle is the ratio of the opposite side to the adjacent side.<\/p>\n

5.\u00a0For example, the sine of an angle is equal to the cosine of its complement; the cosine of an angle is equal to the sine of its complement.<\/p>\n

7.\u00a0[latex]\\frac{\\pi }{6}[\/latex]<\/p>\n

9.\u00a0[latex]\\frac{\\pi }{4}[\/latex]<\/p>\n

11.\u00a0[latex]b=\\frac{20\\sqrt{3}}{3},c=\\frac{40\\sqrt{3}}{3}[\/latex]<\/p>\n

13.\u00a0[latex]a=10,000,c=10,000.5[\/latex]<\/p>\n

15.\u00a0[latex]b=\\frac{5\\sqrt{3}}{3},c=\\frac{10\\sqrt{3}}{3}[\/latex]<\/p>\n

17.\u00a0[latex]\\frac{5\\sqrt{29}}{29}[\/latex]<\/p>\n

19.\u00a0[latex]\\frac{5}{2}[\/latex]<\/p>\n

21.\u00a0[latex]\\frac{\\sqrt{29}}{2}[\/latex]<\/p>\n

23.\u00a0[latex]\\frac{5\\sqrt{41}}{41}[\/latex]<\/p>\n

25.\u00a0[latex]\\frac{5}{4}[\/latex]<\/p>\n

27.\u00a0[latex]\\frac{\\sqrt{41}}{4}[\/latex]<\/p>\n

29.\u00a0[latex]c=14, b=7\\sqrt{3}[\/latex]<\/p>\n

31.\u00a0[latex]a=15, b=15[\/latex]<\/p>\n

33.\u00a0[latex]b=9.9970, c=12.2041[\/latex]<\/p>\n

35.\u00a0[latex]a=2.0838, b=11.8177[\/latex]<\/p>\n

37.\u00a0[latex]a=55.9808,c=57.9555[\/latex]<\/p>\n

39.\u00a0[latex]a=46.6790,b=17.9184[\/latex]<\/p>\n

41.\u00a0[latex]a=16.4662,c=16.8341[\/latex]<\/p>\n

43.\u00a0188.3159<\/p>\n

45.\u00a0200.6737<\/p>\n

47.\u00a0498.3471 ft<\/p>\n

49.\u00a01060.09 ft<\/p>\n

51.\u00a027.372 ft<\/p>\n

53.\u00a022.6506 ft<\/p>\n

55.\u00a0368.7633 ft<\/p>\n

56.\u00a0[latex]{7.2}^{\\circ }[\/latex]<\/p>\n

58.\u00a0[latex]{5.7}^{\\circ }[\/latex]<\/p>\n

60.\u00a0[latex]{82.4}^{\\circ }[\/latex]<\/p>\n

62.\u00a0[latex]{31.0}^{\\circ }[\/latex]<\/p>\n

64.\u00a0[latex]{88.7}^{\\circ }[\/latex]<\/p>\n

66.\u00a0[latex]{59.0}^{\\circ }[\/latex]<\/p>\n

68.\u00a0[latex]{36.9}^{\\circ }[\/latex]<\/p>\n\n\t\t\t

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Candela Citations<\/h3>\n\t\t\t\t\t
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CC licensed content, Specific attribution<\/div>