Aship sails 200 km on a bearing of 243.7 degrees.
(a) how far south has it travelled?
(b) how far west has it travelled?

Step-by-step explanation:

The bearing is always measured from the North direction so when we say that the bearing is 243.7 degrees , It means that the ship has sailed in the direction clockwise of North to  243.7 degrees .

a.

When we try to find the distance it has traveled towards south the cos component is used .

so the Ship traveled = 200 cos (243.7) = - 88.61

Negative value represents the opposite direction from North so we say that

Ship has traveled 88.61 km south .

b.

Now the west direction distance can be found by using the sin component

so the distance traveled in the west direction is

200 sin(243.7) =179.30 km

Ship has traveled 179.30 km west .

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752

d. corresponding side lengths in similar triangles are proportional in length.

step-by-step explanation: