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>Bài 27 (Trang 88, SGK Toán Hình học 9, Tập 1):</strong></p>
<p>Cho tam giác ABC vuông tại A, tính các cạnh và các góc của tam giác ABC, biết:</p>
<p>a) b = 10cm, góc C = 30<sup>o</sup>;</p>
<p>b) c = 10cm, góc C = 45<sup>o</sup>;</p>
<p>c) a = 20cm, góc B = 35<sup>o</sup>;</p>
<p>d) c = 21cm, b = 18cm.</p>
<p> </p>
<p><strong><span style="text-decoration: underline;"><em>Hướng dẫn giải:</em></span></strong></p>
<p>a) <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi mathvariant="normal">B</mi><mo>^</mo></mover><mo> </mo><mo>=</mo><mo> </mo><mn>90</mn><mo>°</mo><mo> </mo><mo>-</mo><mo> </mo><mover><mi mathvariant="normal">C</mi><mo>^</mo></mover><mo> </mo><mo>=</mo><mo> </mo><mn>60</mn><mo>°</mo><mo>,</mo><mo> </mo><mi mathvariant="normal">c</mi><mo> </mo><mo>=</mo><mo> </mo><mi mathvariant="normal">b</mi><mo>.</mo><mi>tg</mi><mo> </mo><mover><mi mathvariant="normal">C</mi><mo>^</mo></mover><mo> </mo><mo>=</mo><mo> </mo><mn>5</mn><mo>,</mo><mn>774</mn><mo> </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> </mo><mo>=</mo><mo> </mo><mfrac><mi mathvariant="normal">b</mi><mrow><mi>sin</mi><mo> </mo><mover><mi mathvariant="normal">B</mi><mo>^</mo></mover></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>10</mn><mrow><mi>sin</mi><mo> </mo><mn>60</mn><mo>°</mo></mrow></mfrac><mo> </mo><mo>≈</mo><mo> </mo><mn>11</mn><mo>,</mo><mn>547</mn><mo> </mo><mo>(</mo><mi>cm</mi><mo>)</mo></math></p>
<p>b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi mathvariant="normal">B</mi><mo>^</mo></mover><mo> </mo><mo>=</mo><mo> </mo><mn>90</mn><mo>°</mo><mo> </mo><mo>-</mo><mo> </mo><mover><mi mathvariant="normal">C</mi><mo>^</mo></mover><mo> </mo><mo>=</mo><mo> </mo><mn>45</mn><mo>°</mo><mo>,</mo><mo> </mo><mi mathvariant="normal">b</mi><mo> </mo><mo>=</mo><mo> </mo><mi mathvariant="normal">c</mi><mo> </mo><mo>=</mo><mo> </mo><mn>10</mn><mi>cm</mi><mo>,</mo><mo> </mo><mi mathvariant="normal">a</mi><mo> </mo><mo>=</mo><mo> </mo><mn>10</mn><msqrt><mn>2</mn></msqrt><mo> </mo><mo>≈</mo><mo> </mo><mn>14</mn><mo>,</mo><mn>142</mn><mo> </mo><mo>(</mo><mi>cm</mi><mo>)</mo></math></p>
<p>c) <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi mathvariant="normal">C</mi><mo>^</mo></mover><mo> </mo><mo>=</mo><mo> </mo><mn>90</mn><mo>°</mo><mo> </mo><mo>-</mo><mo> </mo><mover><mi mathvariant="normal">B</mi><mo>^</mo></mover><mo> </mo><mo>=</mo><mo> </mo><mn>55</mn><mo>°</mo><mo>;</mo><mo> </mo><mi mathvariant="normal">b</mi><mo> </mo><mo>=</mo><mo> </mo><mi mathvariant="normal">a</mi><mo>.</mo><mi>sin</mi><mo> </mo><mover><mi mathvariant="normal">B</mi><mo>^</mo></mover><mo> </mo><mo>=</mo><mo> </mo><mn>20</mn><mo>.</mo><mi>sin</mi><mo> </mo><mn>35</mn><mo>°</mo><mo> </mo><mo>≈</mo><mo> </mo><mn>11</mn><mo>,</mo><mn>472</mn><mo> </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> </mo><mi mathvariant="normal">a</mi><mo>.</mo><mi>sin</mi><mo> </mo><mover><mi mathvariant="normal">C</mi><mo>^</mo></mover><mo> </mo><mo>=</mo><mo> </mo><mn>20</mn><mo>.</mo><mi>sin</mi><mo> </mo><mn>55</mn><mo>°</mo><mo> </mo><mo>≈</mo><mo> </mo><mn>16</mn><mo>,</mo><mn>383</mn><mo> </mo><mo>(</mo><mi>cm</mi><mo>)</mo></math></p>
<p>d) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tg</mi><mo> </mo><mover><mi mathvariant="normal">B</mi><mo>^</mo></mover><mo> </mo><mo>=</mo><mo> </mo><mfrac><mi mathvariant="normal">b</mi><mi mathvariant="normal">c</mi></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>6</mn><mn>7</mn></mfrac><mo> </mo><mo>⇒</mo><mo> </mo><mover><mi mathvariant="normal">B</mi><mo>^</mo></mover><mo> </mo><mo>≈</mo><mo> </mo><mn>41</mn><mo>°</mo><mo>;</mo><mo> </mo><mover><mi mathvariant="normal">C</mi><mo>^</mo></mover><mo> </mo><mo>=</mo><mo> </mo><mn>90</mn><mo>°</mo><mo> </mo><mo>-</mo><mo> </mo><mover><mi mathvariant="normal">B</mi><mo>^</mo></mover><mo> </mo><mo>≈</mo><mo> </mo><mn>49</mn><mo>°</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mi mathvariant="normal">b</mi><mrow><mi>sin</mi><mo> </mo><mi mathvariant="normal">B</mi></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>18</mn><mrow><mi>sin</mi><mo> </mo><mn>41</mn><mo>°</mo></mrow></mfrac><mo> </mo><mo>≈</mo><mo> </mo><mn>27</mn><mo>,</mo><mn>437</mn><mo> </mo><mo>(</mo><mi>cm</mi><mo>)</mo></math>.</p>
Xem lời giải bài tập khác cùng bài