Ben hears from a friend about an underground rave and...

Ben hears from a friend about an underground rave, and invites Austin to come along with him. But when they go to the address they find an empty parking lot with Arianna waiting for them. When Ben and Austin approach Arianna she tells them that to reach the actual rave they must drive a distance of 5 Km in a direction 35 North of East, then travel 4.5 Km in a direction of 280 North of East, then 3.3 Km in a direction 250 North of East, and finally 6.0 Km in a direction 129 North of East. If Arianna doesn't think they were NARCs (and give them bad directions), how far are Ben and Austin they from the rave? In what direction? Group of answer choices (0.03 Km, 266 degrees) (4.28 Km, 143 degrees) (2.17 Km, 82 degrees) (8.63 Km, 193 degrees)

Transcript

00:01 Initial bearing of inn out sign from current location as 10 degree east is given.

00:12 Then shasha takes as 15 degree west route and walks about 1500 feet.

00:21 After that alisa takes 50 degree east route and walks again the same as alisa.

00:36 Then shasha's street bearing to restaurant is south 2 8 degrees east.

00:44 Then alisa's street bearing to restaurant is as 14 degree west.

00:52 Let's solve it step by step.

00:54 Then in the first part of the question we have to calculate the bearings.

00:57 First we will calculate the shasha's bearing it is 180 degree minus 15 degree which is again equal to 165 degrees.

01:08 After that alisa's bearing they are 180 degree plus 50 degree.

01:17 This is equal to 230 degrees.

01:20 So these are the bearings for that.

01:23 After that we have to calculate the displacement.

01:25 Then in the second part of the question we have to calculate the displacement.

01:30 First for shasha's horizontal displacement it is 1500 feet multiplied by cos of 165 degree.

01:40 Then shasha's this was the horizontal displacement.

01:44 Then vertical displacement is 1500 feet multiplied by sin of 165 degrees.

01:53 After that alisa's horizontal displacement it is 1500 feet multiplied by cos of 230 degrees.

02:06 After that its vertical displacement is 1500 multiplied by sin of 230 degree.

02:16 Then shasha's total horizontal displacement is the initial position.

02:25 Its initial position plus the shasha's horizontal displacement and shasha's vertical displacement is nothing but the shasha's total vertical displacement.

02:37 Then alisa's total horizontal displacement it is equal to the initial position plus the alisa's horizontal displacement it will be the total horizontal displacement.

02:51 Then alisa's vertical displacement will be the alisa's vertical displacement it will be the total vertical displacement for alisa.

02:59 Then we have to calculate the bearings to restaurant.

03:02 Then shasha's final bearing to restaurant it is equal to angle whose tangent is nothing but the angle whose tangent is vertical displacement upon the horizontal displacement.

03:20 And for alisa's bearing to restaurant angle whose tangent is vertical displacement divided by horizontal displacement they are same.

03:31 After that next step will be to calculate the remaining distances.

03:36 So, shasha's remaining distance to restaurant is nothing but the horizontal distance displacement square plus vertical displacement square...

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