Two towns that are 32 km apart are 8 cm on a map. What is the scale of the map?
1 answer:
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Answer:
≈ 33°
Step-by-step explanation:
So, first, you can draw a visual. Refer to the image attached below:
Using this info, you can use trigonometric ratios. Recall that:
tangent = opposite side/adjacent side
sine = opposite side/ hypotenuse
cosine = adjacent side/hypotenuse
You can clearly see that you have an opposite side and a given hypotenuse. This means we'll be using sine.
So:
However, we're not trying to find sinX, we're trying to find X.
So we would have to use inverse sine, which would then be:
Put this into your calculator, and:
X ≈ 33.05573115...
9514 1404 393
Answer:
(a) one parallelogram
(b) opposite sides are 3 inches and 4 inches. Opposite angles are 45° and 135°
(c) yes, all side lengths can be determined, see (b)
Step-by-step explanation:
Opposite sides of a parallelogram are the same length, so if one side is 3 inches, so is the opposite side. Similarly, if one side is 4 inches, so is the opposite side. If sides have different lengths, they must be adjacent sides. The given numbers tell us the lengths of all of the sides.
The 4 inch sides are adjacent to the 3 inch sides. Thus the angle between a 4 inch side and a 3 inch side must be 45°. Opposite angles are congruent, and adjacent angles are supplementary, so specifying one angle specifies them all.
Only one parallelogram can be formed with these sides and angles. (The acute angle can be at the left end or the right end of the long side. This gives rise to two possible congruent orientations of the parallelogram. Because these are congruent, we claim only one parallelogram is possible. Each is a reflection of the other.)
