Tell whether the figure is a polygon. If it is a polygon,
1 answer:
Answers:
- Polygon? <u>Yes</u>
- Classify: <u>Pentagon</u>
- The polygon is <u>concave</u>
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Explanation:
The figure is a polygon because it's composed of straight lines only, and we have a closed loop (or enclosed area).
This is a pentagon since it has 5 sides
The pentagon is concave because of the angle kicked in up top that caves in, so to speak. This interior angle exceeds 180 degrees and is known as a reflex angle.
Here's another way to determine the figure is concave: It's possible to pick two points inside the polygon such that the segment formed between them crosses outside the boundaries. See the diagram below.
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Answer:
69.01 m
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you ...
Tan = Opposite/Adjacent
The tangent function is useful for problems like this. Let the height of the spire be represented by h. The distance (d) across the plaza from the first surveyor satisfies the relation ...
tan(50°) = (h -1.65)/d
Rearranging to solve for d, we have ...
d = (h -1.65)/tan(50°)
The distance across the plaza from the second surveyor satisfies the relation ...
tan(30°) = (101.65 -h)/d
Rearranging this, we have ...
d = (101.65 -h)/tan(30°)
Equating these expressions for d, we can solve for h.
(h -1.65)/tan(50°) = (101.65 -h)/tan(30°)
h(1/tan(50°) +1/tan(30°)) = 101.65/tan(30°) +1.65/tan(50°)
We can divide by the coefficient of h and simplify to get ...
h = (101.65·tan(50°) +1.65·tan(30°))/(tan(30°) +tan(50°))
h ≈ 69.0148 ≈ 69.01 . . . . meters
The tip of the spire is 69.01 m above the plaza.
