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.

Patrick is 177.809 feet from Johnny

The bearing of Patrick from Johnny is 215.5186°

Step-by-step 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°

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option

51-50

step-by-step explanation: