158k views
2 votes
4.) Johnny picks up a baseball and throws it to Rob who is exactly 130 feet away at a direction of 50 degrees. Rob then throws the ball to Patrick who is 50 feet from Rob in a direction of 30 degrees. Find the exact distance and direction that Patrick is from Johnny.

1 Answer

0 votes

Answer:

Patrick is 177.809 feet from Johnny

The bearing of Patrick from Johnny is 215.5186°

Explanation:

The length of Johnny to Patrick let's assume it's x.

The angle opposite x is =

(90-50)+90+30

= 160°

To look for x

X² = A² + B² - 2ABcosx

Where A and B are the distance of Johnny to Rob and Rob to Patrick respectively.

X² = 130² + 50² - 2(130)(50)cos160

X²= 16900 + 2500 + 12216.004

X² = 31616.004

X= 177.809

The direction using sine rule .

Let the direction be y

50/siny = 177.809/sin160

50/siny = 177.809/0.342

50/siny = 519.9094

Siny = 50/519.904

Siny= 0.09617

Y = sin^-1(0.09617)

Y = 5.5186

The bearing of Patrick from Johnny is 5.5186 + 30 + 180

= 215.5186°

User IgorekPotworek
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories