Question

7. Assume two people, Swanson and Suzie, are standing 35 feet apart and are watching a boat

race. At a given moment, Swanson approximates the angle formed by the lead boat, himself, and
Suzie to be 30°. Suzie approximates the angle formed by the lead boat, herself, and Swanson to be
130. How far is the boat from Swanson?
130°
30"
35 feet
Swanson
Suzie
Part I: What is the missing angle in this triangle? (1 point)
Part II: Use the law of sines to find the distance from Swanson to the boat. (2 points)

Answer 1

78.4 ft hope this helped good luck on the test or quiz or whatever it is good luck

Answer 2

78.4 ft

Explanation:

Part I:

Missing angle = 180° - (130 + 30) (sum of angles in a triangle)

= 180° - 160°

Missing angle = 20°

Part II: distance (d) from Swanson to the boat

Law of Sines is given as:

`(a)/(sin(A)) = (b)/(sin(B))`

Where,

a = d

A = 130°

b = 35 ft

B = 20°

Plug in the values and solve for d

`(d)/(sin(130)) = (35)/(sin(20))`

Multiply both sides by sin(130) to make d the subject of the formula

`(d)/(sin(130))*sin(130) = (35)/(sin(20))*sin(130)`

`d = (35*sin(130))/(sin(20))`

`d = 78.4 ft`