An artist makes necklaces. She packs each necklace in a small jewelry box that is134inches by 214 inches by 34 inch. A departmen
1 answer:
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Answer:
Approximately (assuming that the height of the base of the hill is the same as that of the observer.)
Step-by-step explanation:
Refer to the diagram attached.
- Let
denote the observer.
- Let
denote the top of the tree.
- Let
denote the base of the tree.
- Let
denote the point where line
(a vertical line) and the horizontal line going through
.
Angles:
- Angle of elevation of the base of the tree as it appears to the observer:
.
- Angle of elevation of the top of the tree as it appears to the observer:
.
Let the length of segment (vertical distance between the base of the tree and the base of the hill) be
.
The question is asking for the length of segment . Notice that the length of this segment is
.
The length of segment could be represented in two ways:
- In right triangle
as the side adjacent to
- In right triangle
as the side adjacent to
For example, in right triangle , the length of the side opposite to
is segment
. The length of that segment is
.
.
Rearrange to find an expression for the length of (in
) in terms of
:
.
Similarly, in right triangle :
.
Equate the right-hand side of these two equations:
.
Solve for :
.
Hence, the height of the top of this tree relative to the base of the hill would be .
