Bài 4: Một số hệ thức về cạnh và góc trong tam giác vuông
Hướng dẫn Giải Bài 27 (Trang 88, SGK Toán Hình học 9, Tập 1)
<p><strong>B&agrave;i 27 (Trang 88, SGK To&aacute;n H&igrave;nh học 9, Tập 1):</strong></p> <p>Cho tam gi&aacute;c ABC vu&ocirc;ng tại A, t&iacute;nh c&aacute;c cạnh v&agrave; c&aacute;c g&oacute;c của tam gi&aacute;c ABC, biết:</p> <p>a) b = 10cm, g&oacute;c C = 30<sup>o</sup>;</p> <p>b) c = 10cm, g&oacute;c C = 45<sup>o</sup>;</p> <p>c) a = 20cm, g&oacute;c B = 35<sup>o</sup>;</p> <p>d) c = 21cm, b = 18cm.</p> <p>&nbsp;</p> <p><strong><span style="text-decoration: underline;"><em>Hướng dẫn giải:</em></span></strong></p> <p>a)&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi mathvariant="normal">B</mi><mo>^</mo></mover><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>90</mn><mo>&#176;</mo><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mover><mi mathvariant="normal">C</mi><mo>^</mo></mover><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>60</mn><mo>&#176;</mo><mo>,</mo><mo>&#160;</mo><mi mathvariant="normal">c</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mi mathvariant="normal">b</mi><mo>.</mo><mi>tg</mi><mo>&#160;</mo><mover><mi mathvariant="normal">C</mi><mo>^</mo></mover><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>5</mn><mo>,</mo><mn>774</mn><mo>&#160;</mo><mo>(</mo><mi>cm</mi><mo>)</mo></math></p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mi mathvariant="normal">b</mi><mrow><mi>sin</mi><mo>&#160;</mo><mover><mi mathvariant="normal">B</mi><mo>^</mo></mover></mrow></mfrac><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mn>10</mn><mrow><mi>sin</mi><mo>&#160;</mo><mn>60</mn><mo>&#176;</mo></mrow></mfrac><mo>&#160;</mo><mo>&#8776;</mo><mo>&#160;</mo><mn>11</mn><mo>,</mo><mn>547</mn><mo>&#160;</mo><mo>(</mo><mi>cm</mi><mo>)</mo></math></p> <p>b)&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi mathvariant="normal">B</mi><mo>^</mo></mover><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>90</mn><mo>&#176;</mo><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mover><mi mathvariant="normal">C</mi><mo>^</mo></mover><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>45</mn><mo>&#176;</mo><mo>,</mo><mo>&#160;</mo><mi mathvariant="normal">b</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mi mathvariant="normal">c</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>10</mn><mi>cm</mi><mo>,</mo><mo>&#160;</mo><mi mathvariant="normal">a</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>10</mn><msqrt><mn>2</mn></msqrt><mo>&#160;</mo><mo>&#8776;</mo><mo>&#160;</mo><mn>14</mn><mo>,</mo><mn>142</mn><mo>&#160;</mo><mo>(</mo><mi>cm</mi><mo>)</mo></math></p> <p>c)&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi mathvariant="normal">C</mi><mo>^</mo></mover><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>90</mn><mo>&#176;</mo><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mover><mi mathvariant="normal">B</mi><mo>^</mo></mover><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>55</mn><mo>&#176;</mo><mo>;</mo><mo>&#160;</mo><mi mathvariant="normal">b</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mi mathvariant="normal">a</mi><mo>.</mo><mi>sin</mi><mo>&#160;</mo><mover><mi mathvariant="normal">B</mi><mo>^</mo></mover><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>20</mn><mo>.</mo><mi>sin</mi><mo>&#160;</mo><mn>35</mn><mo>&#176;</mo><mo>&#160;</mo><mo>&#8776;</mo><mo>&#160;</mo><mn>11</mn><mo>,</mo><mn>472</mn><mo>&#160;</mo><mo>(</mo><mi>cm</mi><mo>)</mo></math></p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">c</mi><mo>=</mo><mo>&#160;</mo><mi mathvariant="normal">a</mi><mo>.</mo><mi>sin</mi><mo>&#160;</mo><mover><mi mathvariant="normal">C</mi><mo>^</mo></mover><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>20</mn><mo>.</mo><mi>sin</mi><mo>&#160;</mo><mn>55</mn><mo>&#176;</mo><mo>&#160;</mo><mo>&#8776;</mo><mo>&#160;</mo><mn>16</mn><mo>,</mo><mn>383</mn><mo>&#160;</mo><mo>(</mo><mi>cm</mi><mo>)</mo></math></p> <p>d)&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tg</mi><mo>&#160;</mo><mover><mi mathvariant="normal">B</mi><mo>^</mo></mover><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mi mathvariant="normal">b</mi><mi mathvariant="normal">c</mi></mfrac><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mn>6</mn><mn>7</mn></mfrac><mo>&#160;</mo><mo>&#8658;</mo><mo>&#160;</mo><mover><mi mathvariant="normal">B</mi><mo>^</mo></mover><mo>&#160;</mo><mo>&#8776;</mo><mo>&#160;</mo><mn>41</mn><mo>&#176;</mo><mo>;</mo><mo>&#160;</mo><mover><mi mathvariant="normal">C</mi><mo>^</mo></mover><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>90</mn><mo>&#176;</mo><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mover><mi mathvariant="normal">B</mi><mo>^</mo></mover><mo>&#160;</mo><mo>&#8776;</mo><mo>&#160;</mo><mn>49</mn><mo>&#176;</mo></math></p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mi mathvariant="normal">b</mi><mrow><mi>sin</mi><mo>&#160;</mo><mi mathvariant="normal">B</mi></mrow></mfrac><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mn>18</mn><mrow><mi>sin</mi><mo>&#160;</mo><mn>41</mn><mo>&#176;</mo></mrow></mfrac><mo>&#160;</mo><mo>&#8776;</mo><mo>&#160;</mo><mn>27</mn><mo>,</mo><mn>437</mn><mo>&#160;</mo><mo>(</mo><mi>cm</mi><mo>)</mo></math>.</p>
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