Question

Consider a triangle...

Answer 1

Answer:

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

2. Lake: c = 1105.31 ft

Step-by-step explanation:

Law of Sine Formula:$\frac{sin(A)}{A} = \frac{sin(B)}{B} = \frac{sin(C)}{C}$

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

$\frac{sin(30)}{1.3} = \frac{sin(B)}{1.9} = \frac{sin(C)}{C}$

Solving for sin(B). Cross Multiply.

$\frac{sin(30)}{1.3} = \frac{sin(B)}{1.9}\\1.3*sin(B)=1.9*sin(30)\\sin(B)=\frac{1.9*sin(30)}{1.3}$

B = sin^-1( $\frac{1.9*sin(30)}{1.3}$ )

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)

$\frac{sin(30)}{1.3} = \frac{sin(103.05)}{C}$

Cross Multiply

$C*sin(30)=1.3*sin(103.05)\\C=\frac{1.3*sin(103.05)}{sin(30)}$

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.

$c^2=a^2+b^2-2*a*b*cos(C)\\c^2=(850ft)^2+(960ft)^2-2*(850ft)*(960ft)*cos(75)\\\\c=\sqrt{(850ft)^2+(960ft)^2-2*(850ft)*(960ft)*cos(75)\\}$

c ≈ 1105.308698

c = 1105.31 ft