Answer:
5. m∠C ≈ 34°
6. AC ≈ 29.7 metres
Step-by-step explanation:
5. We need to use the Law of Sines here, which says that for a triangle with sides a, b, and c and angles A, B, and C:
[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]
Here, a = 25, ∠A = 93°, and c = 14, so we want to find ∠C:
[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]
[tex]\frac{25}{sin93} =\frac{14}{sinC}[/tex]
sinC ≈ 0.56
∠C ≈ 34°
6. We need to use the Law of Cosines here, which says that for a triangle with sides a, b, and c and angles A, B, and C:
[tex]c^2=a^2+b^2-2abcosC[/tex]
[tex]b^2=a^2+c^2-2accosB[/tex]
[tex]a^2=b^2+c^2-2bccosA[/tex]
Here, a = 23.2, c = 18.1, ∠B = 91°, and b = x. We want to find b, so:
[tex]b^2=a^2+c^2-2accosB[/tex]
[tex]x^2=23.2^2+18.1^2-2*23.2*18.1*cos(91)[/tex] ≈ 880.5
x ≈ 29.7 metres
