Ship A and Ship B are 120 km apart when they pick up a distress call from another boat. Ship B estimates that they are 70 km away from the distress call. They also notice that the angle between the line from ship B to ship A and the line from ship A to the distress call is 28°. What are the two possible distances, to the nearest TENTH of a km, from ship A to the boat?

The two possible distances from Ship A to the distress call boat are 64.4 km and 147.5 km

Step-by-step explanation:

The given parameters are;

The distance between Ship A and Ship B = 120 km

The distance of the distress call from Ship B = 70 km

The angle made between the line from Ship A to B and the line from Ship A to the distress call = 28° = Opposite angle to the line from the location of the distress caller to Ship B

Therefore;

70/(sin(28°)) = 120/(sin(x))

Where;

x = The angle opposite the line from Ship A to B

sin(x) = ((sin(28°))×120)/70 = 0.805

x = sin⁻¹(0.805) = 53.59°

Therefore, the angle opposite the line from Ship A to the distress caller, r = 180 - (28 + 53.59) = 98.4°

From sin rule, we have;

70/(sin(28°)) = r/(sin(98.4°))

r = (70/(sin(28°)))×(sin(98.4°)) = 147.5

However by cosine rule, we have;

70² = 120² + r² - 2×120×r × cos(28°)

4,900 = 14,400 + r² - 211.907·r

r² - 211.907·r + 14,400 - 4,900 = 0

r² - 211.907·r + 9,500 = 0

Factorizing, we have;

r = 64.406 km or 147.501 km

Which gives;

The distance of the line from Ship A to the distress caller =  64.4 km or 147.5 km to the nearest tenth.

The two possible distances from Ship A to the distress call boat = 64.4 km and 147.5 km

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

c

-by-step explanation:

it would be c