Name the angle of elevation and the angle of depression in the figure below. Compare the measures of these angles. Explain.

Given:

Given that AB and CD are parallel lines.

The line CB makes and angle at B and C.

We need to determine the angle of elevation and the angle of depression.

Angle of elevation:

The upward angle to the line of sight from the horizontal line is called the angle of elevation.

From the given figure, the upward angle from the horizontal line is ∠BCD

Thus, ∠BCD is the angle of elevation.

Angle of depression:

The downward angle to the line of sight from the horizontal line is called the angle of depression.

From the given figure, the downward angle from the horizontal line is ∠ABC

Thus, ∠ABC is the angle of depression.

Comparison of two angles:

The angle of elevation is ∠BCD and the angle of depression is ∠ABC

Comparing the two angles, the angles of elevation and depression are always congruent.

Hence, ∠BCD = ∠ABC

Thus, the angle of elevation and the angle of depression are congruent.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

the answer is: the length is 5/6 yards.

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step-by-step explanation: