Answer:
4. 14.03 miles
5. 15.02 kilometers
6. 19.95 meters
Step-by-step explanation:
4. We need to use the law of sines, which states that for a triangle with angles A, B, and C and sides a, b, and c, respectively, then:
[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]
Here, a = 30, <A = 130, and <B = 21. So, let's plug these in:
[tex]\frac{30}{sin130} =\frac{b}{sin21}[/tex]
b = AC = [tex]\frac{30}{sin130}*{sin21}[/tex] ≈ 14.03 miles
5. Here, c = 7, <C = 23, and <A = 123. We want to find BC, which is just a:
[tex]\frac{7}{sin23} =\frac{a}{sin123}[/tex]
a = BC = [tex]\frac{7}{sin23} *{sin123}[/tex] ≈ 15.02 kilometers
6. Here, c = 22, <C = 88, and <B = 65. We want to find AC, which is just b:
[tex]\frac{22}{sin88} =\frac{b}{sin65}[/tex]
b = AC = [tex]\frac{22}{sin88} *{sin65}[/tex] ≈ 19.95 meters
Hope this helps!
