From the observation deck of the lighthouse at Sasquatch Point 55 feet above the surface of Lake Ippizuti, a lifeguard spots a boat out on the lake sailing directly toward the light house. The first sighting had a angle of depression of 8.1 and the second sighting had an angle of depression of 25.7°. How far had the boat traveled between the sightings?

272.17 ft

Step-by-step explanation:

Since the angle of depression of the sighting equals the angle of elevation of the lighthouse from the boat, using trigonometric ratios,

tanθ = x/d where θ = angle of sighting, x = height of lighthouse =55 ft and d = distance of boat from lighthouse at sighting

So, d = x/tanθ

when θ = 8.1°, for the first sighting,

d₁ = 55/tan8.1 = 386.45 ft

when θ = 25.7°, for the second sighting,

d₂ = 55/tan8.1 = 114.28 ft

The distance the boat traveled between the two sightings is thus d₁ - d₂ = 386.45 ft - 114.28 ft = 272.17 ft

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