Question

Consider a triangle...

Answer 1

1. Triangle: B = 47.0° , C = 103.05° , c = 2.53 cm

2. Lake: c = 1105.31 ft

Explanation:

Law of Sine Formula:
`(sin(A))/(A) = (sin(B))/(B) = (sin(C))/(C)`

Given: A = 30° , a = 1.3 cm , b = 1.9 cm

`(sin(30))/(1.3) = (sin(B))/(1.9) = (sin(C))/(C)`

Solving for sin(B). Cross Multiply.

`(sin(30))/(1.3) = (sin(B))/(1.9)\\1.3*sin(B)=1.9*sin(30)\\sin(B)=(1.9*sin(30))/(1.3) \\`

B = sin^-1(
`(1.9*sin(30))/(1.3)` )

B ≈ 46.9509202

B = 47.0°

Solve for C°

A° + B° + C° = 180°

30° + 46.95° + C° = 180°

C° = 180° - 30° - 46.95°

C° = 103.05°

Solve for sin(C)

`(sin(30))/(1.3) = (sin(103.05))/(C)\\`

Cross Multiply

`C*sin(30)=1.3*sin(103.05)\\C=(1.3*sin(103.05))/(sin(30))`

C ≈ 2.532850806

C = 2.53 cm

Law of Cosine Formula:
`c^2=a^2+b^2-2*a*b*cos(C)`

Given: a = 850 ft , b = 960 ft , C=75°

Solve for c.

`c^2=a^2+b^2-2*a*b*cos(C)\\c^2=(850ft)^2+(960ft)^2-2*(850ft)*(960ft)*cos(75)\\\\c=√((850ft)^2+(960ft)^2-2*(850ft)*(960ft)*cos(75)\\) \\`

c ≈ 1105.308698

c = 1105.31 ft