Question

a boat leaves at noon and has a bearing of S 35 east. The boat travels at 40 miles per hour. (a) many miles south and how many miles east will the boat have traveled at 7 pm

Answer 1

Answer:

South =34.18 miles

East=  49.12miles

Step-by-step explanation:

We begin by calculating the distance covered in 7n hours

that is from 12 pm to 7pm which is 7 hours

so time t= 7 hours

speed= 40 miles per hours

we know that speed= distance/time

let the distance be x

40=x/7

x=40*7

x=28miles

(a) many miles south and how many miles east will the boat have traveled at 7 pm

applying SOH CAH TAO we have

For the  south  CAH

cos Ф=hyp/adj

hyp= 28 mile

Ф= 35°

cos 35= 28/adj

0.819=28/adj

adj=28/0.819

adj=34.18 miles

For the  East SOH

sin Ф=hyp/opp

hyp= 28 mile

Ф= 35°

sin 35= 28/opp

0.57=28/opp

opp=28/0.57

opp=49.12miles