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(Two office buildings are 51 m apart. The height of the taller building is 207 m. The angle of depression from the top of the taller building to the top of the shorter building is 15 degrees. Find the height of the shorter building to the nearest meter. )

QUESTION
In the previous problem how does the angle of depression from the top of the taller building relate to the angle of elevation from the top of the shorter building. (You can pick more than once choice)

A:They are congruent
B:They are complementary
C:They are supplementary
D:They are alternate interior angles
E:They are alternate exterior angles
F:They are corresponding angles.

Respuesta :

calculista
see the attached figure to better understand the problem

we know that

in the triangle ABC
tan 15=AC/BC--------> AC=BC*tan 15
BC=51 m
AC=51*tan 15------> AC=13.67 m

the height of the shorter building=207-AC----> 207-13.67----> 193.33 m
the height of the shorter building=193 m

the answer Part a) is
the height of the shorter building is 193 m

Part b) how does the angle of depression from the top of the taller building relate to the angle of elevation from the top of the shorter building

we know that

the angle of depression is equals to the angle of elevation
so

the answers are
A:They are congruent
D:They are alternate interior angles
Ver imagen calculista

Angle of depression from top of the taller building relate to angle of elevation from, top of the shorter building as they are congruent and  alternate interior angles.

What is angle of depression and elevation?

The angle of depression is the angle made between the straight line and the line of observer seeing the object, which is below that straight line.

The angle of elevation is the angle made between the straight line and the line of observer seeing the object, which is above that straight line.

The distance between the two office building is equal to the 51 meters and the angle of depression from the top of the taller building to the top of the shorter building is 15 degrees.  

In the image attached below, the triangle shown is the right angle triangle. The tangent of the right angle is the ratio of the opposite side to the base. Therefore,

[tex]tan(15)=\dfrac{x}{51}\\x=13.67\rm m[/tex]

The height of the taller building is 207 m. Thus, the height of the shorter building is,

[tex]h=207-x\\h=207-13.67\\h\cong193 \rm m[/tex]

Thus, the height of the smaller building is 193 meters.

The angle of elevation is congruent to the angle of depression and both are alternate interior angles.

Thus, angle of depression from the top of the taller building relate to the angle of elevation from the top of the shorter building as they are congruent and  alternate interior angles. The height of the smaller building is 193 meters.

Learn more about the angle of depression here;

https://brainly.com/question/10217662

Learn more about the angle of elevation here;

https://brainly.com/question/2004882

Ver imagen bhoopendrasisodiya34

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