第一题第(1)小题我算到a约等于19有没有错啊?
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/08/28 01:33:02
第一题第(1)小题我算到a约等于19有没有错啊?
![](http://img.wesiedu.com/upload/e/d5/ed5cd09f546a7d168aef75b6d36923f5.jpg)
![](http://img.wesiedu.com/upload/e/d5/ed5cd09f546a7d168aef75b6d36923f5.jpg)
1、
![](http://img.wesiedu.com/upload/8/b9/8b97b64255862bbbbdd42bc587b02eef.jpg)
(1).∠B=180°-30°-45°=180°-75°,sin(180°-75°)=sin75°=sin(90°-15°)=cos15°,
cos15°=(√6+√2)/4.
a/sin45°=c/sin30°,a=(10*√2/2)/(1/2)=10√2.
b/sin105°=c/sin30°,b=c*sin105°/sin30°=c*cos15°/sin30°=[10*(√6+√2)/4]/(1/2)=5*(√6+√2)
∠A=45°
∠B=105°
∠C=30°
a=10√2≈14cm
b=5(√6+√2)≈19cm
c=10cm
![](http://img.wesiedu.com/upload/9/c3/9c3a330b8d7ca6f7e21fcae489f1bf62.jpg)
(2).sin75°=sin(90°-15°)=cos15°=(√6+√2)/4.
a/sin60°=c/sin75°, a=(20*√3/2)/[(√6+√2)/4]=10(3√2-√6)≈18.
b/sin45°=a/sin60°, b=(18*√2/2)/(√3/2)=(6*√6)≈15.
∠A=60°
∠B=45°
∠C=75°
a≈18cm
b≈15cm
c=20cm
2、
(1).
![](http://img.wesiedu.com/upload/4/5d/45df0caffc344c28e2baa63db2be307b.jpg)
sinA/a=sinB/b,sinA=a*sibB/b=(20*1/2)/11=10/11=0.909,∠A≈65°,∠C=180°-30°-65°=85°,
sinC=sin85°=0.996
c/sinC=b/sinB, c=b*sinC/sinB=(11*0.996)/(1/2)≈22.
∠A=65°
∠B=30°
∠C=85°
a=20cm
b=11cm
c=22cm
(2).
![](http://img.wesiedu.com/upload/e/b7/eb7838a6681a733b9ea765194b5417c0.jpg)
sin115°=sin(180°-65°)=sin65°=0.9063
sinC/c=sinB/b,sinB=b*sinC/c=(39*0.9063)/54=0.655,∠B=41°,∠A=180°-115°-41°=24°.
a/sinA=c/sinC,a=c*sinA/sinC=(54*0.407)/0.9063≈24.
∠A=24°
∠B=41°
∠C=115°
a=24cm
b=39cm
c=54cm
![](http://img.wesiedu.com/upload/8/b9/8b97b64255862bbbbdd42bc587b02eef.jpg)
(1).∠B=180°-30°-45°=180°-75°,sin(180°-75°)=sin75°=sin(90°-15°)=cos15°,
cos15°=(√6+√2)/4.
a/sin45°=c/sin30°,a=(10*√2/2)/(1/2)=10√2.
b/sin105°=c/sin30°,b=c*sin105°/sin30°=c*cos15°/sin30°=[10*(√6+√2)/4]/(1/2)=5*(√6+√2)
∠A=45°
∠B=105°
∠C=30°
a=10√2≈14cm
b=5(√6+√2)≈19cm
c=10cm
![](http://img.wesiedu.com/upload/9/c3/9c3a330b8d7ca6f7e21fcae489f1bf62.jpg)
(2).sin75°=sin(90°-15°)=cos15°=(√6+√2)/4.
a/sin60°=c/sin75°, a=(20*√3/2)/[(√6+√2)/4]=10(3√2-√6)≈18.
b/sin45°=a/sin60°, b=(18*√2/2)/(√3/2)=(6*√6)≈15.
∠A=60°
∠B=45°
∠C=75°
a≈18cm
b≈15cm
c=20cm
2、
(1).
![](http://img.wesiedu.com/upload/4/5d/45df0caffc344c28e2baa63db2be307b.jpg)
sinA/a=sinB/b,sinA=a*sibB/b=(20*1/2)/11=10/11=0.909,∠A≈65°,∠C=180°-30°-65°=85°,
sinC=sin85°=0.996
c/sinC=b/sinB, c=b*sinC/sinB=(11*0.996)/(1/2)≈22.
∠A=65°
∠B=30°
∠C=85°
a=20cm
b=11cm
c=22cm
(2).
![](http://img.wesiedu.com/upload/e/b7/eb7838a6681a733b9ea765194b5417c0.jpg)
sin115°=sin(180°-65°)=sin65°=0.9063
sinC/c=sinB/b,sinB=b*sinC/c=(39*0.9063)/54=0.655,∠B=41°,∠A=180°-115°-41°=24°.
a/sinA=c/sinC,a=c*sinA/sinC=(54*0.407)/0.9063≈24.
∠A=24°
∠B=41°
∠C=115°
a=24cm
b=39cm
c=54cm