问题详情

计算题:如图所示,已知a=7m,b=6m,c=3m,求∠A,∠B,∠C?


时间:2021-12-30 05:58 关键词: 水工监测工(初级) 水工监测工

答案解析

<p> 由余弦定理得:<br> cosA=(b<sup>2</sup>+c<sup>2</sup>-a<sup>2</sup>)/2bc=(62+32-72)/2&times;6&times;3=-0.1111111;<br> &ang;A=arccos(-0.1111111)=96&deg;22&prime;45.7&Prime;;<br> cosB=(a<sup>2</sup>+c<sup>2</sup>-b<sup>2</sup>)/2ac=(72+32-62)/2&times;7&times;3=0.5238095;<br> &ang;B=arccos0.5238095=58&deg;24&prime;42.7&Prime;;<br> &ang;C=180&deg;-(&ang;A+&ang;B)=180&deg;-(96&deg;22&prime;45.7&Prime;+58&deg;24&prime;42.7&Prime;)=25&deg;12&prime;31.6&Prime;</p>