Do these ratios form a proportion? 26 medium hats to 2 small hats 39 medium hats to 3 small hats
2 answers:
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Answer:
A: 3/4
Step-by-step explanation:
sine is the length of the opposite side / length the hypotenuse side
cosine is the length of the adjacent side / length the hypotenuse side
using what's given:
- the opposite side has a length of 3
- the adjacent side has a length of 4
- the hypotenuse side has a length of 5
Tangent is the ratio between the opposite side length and the adjacent side length (opp/adj). With our givens, this means tan(A) = 3/4. See image for more.
Explanation:
a. The line joining the midpoints of the parallel bases is perpendicular to both of them. It is the line of symmetry for the trapezoid. This means the angles and sides on one side of that line of symmetry are congruent to the corresponding angles and sides on the other side of the line. The diagonals are the same length.
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b. We observe that adjacent pairs of points have the same x-coordinate, so are on vertical lines, which have undefined slope. KN is a segment of the line x=1; LM is a segment of the line x=3. If the trapezoid is isosceles, the midpoints of these segments will be on a horizontal line. The midpoint of KN is at y=(3-2)/2 = 1/2. The midpoint of LM is at y=(1+0)/2 = 1/2. These points are on the same horizontal line, so the trapezoid <em>is isosceles</em>.
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c. We observed in part (b) that the parallel sides are KN and LM. The coordinate difference between K and L is (1, 3) -(3, 1) = (-2, 2). That is, segment KL is the hypotenuse of an isosceles right triangle with side lengths 2, so the lengths of KL and MN are both 2√2.
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For part (c), we used the shortcut that the hypotenuse of an isosceles right triangle is √2 times the leg length.
