geometry question

Question

There is a tree standing in the desert; the sun is rising to the East.

a. As the sun peaks over a plateau and hits the tree, classify the angle the shadow of the tree makes with the ground.
b. As the sun continues to move across the sky, classify the different types of angles that will be created and explain why they will be created.
c. When are acute angles created?
d. When would a right angle be created?
e. When would an obtuse angle be created?
f. Would there ever be a straight angle created?
g. Estimate the size of the angle when the sun is at midmorning.

Answer 1

Hi,

 

Perhaps there is a very significant typo -- 'peeks' is like peekaboo, but 'peaks' means to achieve a high point.

 

Also, the angle of the shadow (on the ground) makes with the ground, is always zero, but let's assume that the sun (rising in, not to, the east) makes a shadow at some angle of interest.

 

[a] When peeking (sunrise), the sun creates an angle of 180 degrees (a straight line) -- sun to tree to shadow.

 

[b] During the morning, the sun-tree-shadow decreases from 180 to 90 (obtuse) until "high noon" (perpendicular, 90 degrees).  Then, the angle continues to decrease from 90 to 0 (acute angles) at sunset (on a flat plateau).

 

[c] Acute angles occur all afternoon.

 

[d] A right angle (90 degrees) occurs at noon.

 

[e] Obtuse angles occur all morning.

 

[f] A very-nearly straight angle occurs at sunrise (note: to be exactly straight, it must follow the ground exactly)

 

[g] At mid-morning, the sun-tree-shadow is precisely (not estimated) 135 degrees   (45+90)