Question 1:
Look at the first attached image.
We want to solve for the height of the smaller building. Let's start by making a right triangle with angle of 15 degrees and adjacent side of 51 m.
Let's solve for the other leg. Multiply the tangent with 51 m to get the length of the other leg.
[tex]51*tan(15)[/tex]
[tex]\approx 14[/tex]
Now, subtract that from 207 to get the height of the smaller building.
[tex]207-14=193[/tex]
That's your answer.
Question 2:
The angle of elevation is congruent to the angle of depression because they are alternate interior angles.
Thus, you can choose the 1st and 4th choices as your answer.
Question 3:
Look at the second attached image.
Angle E is congruent to angle D for the same reasons mentioned in the last question.
We can create an equation.
[tex]3x+1=2(x+8)[/tex]
Distributive property
[tex]3x+1=2x+16[/tex]
Subtract both sides by 1 and 2x
[tex]x=15[/tex]
Since E and D are congruent, just plug this value into one of the equations for E or D. You get 46.
The third choice is your answer. Hope this helps! :)
