The side across from the 63° angle is 299.5 ft and the side across from the 56° angle is 278.7 ft.
We will use the Law of Sines to solve this. First, the angle across from the 63° angle:
sin 61/294 = sin 63/x
Cross multiply:
x*sin 61 = 294 sin 63
Divide by sin 61:
(x sin 61)/(sin 61) = (294 sin 63)/(sin 61)
x = 299.5
For the side across from the 56° angle:
sin 61/294 = sin 56/x
Cross multiply:
x*sin 61 = 294 sin 56
Divide both sides by sin 61:
(x sin 61)/(sin 61) = (294 sin 56)/(sin 61)
x = 278.7
Answer:
a. what sequence of transformations 2ill move ∆ABC onto ∆DEF ?
<em>Answer:</em>
Complete proof is written below.
Facts and explanation about the segments shown in question :
- As BC = EF is a given statement in the question
- AB + BC = AC because the definition of betweenness gives us a clear idea that if a point B is between points A and C, then the length of AB and the length of BC is equal to the length of AC. Also according to Segment addition postulate, AB + BC = AC. For example, if AB = 5 and BC= 7 then AC = AB + BC → AC = 12
- AC > BC because the Parts Theorem (Segments) mentions that if B is a point on AC between A and C, then AC > BC and AC>AB. So, if we observe the question figure, we can realize that point B lies on the segment AC between points A and C.
- AC > EF because BC is equal to EF and if AC>BC, then it must be true that the length of AC must greater than the length segment EF.
Below is the complete proof of the observation given in the question:
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<em>STATEMENT REASON </em>
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1. BC = EF 1. Given
2. AB + BC = AC 2. Betweenness
3. AC > BC 3. Def. of segment inequality
4. AC > EF 4. Def. of congruent segments
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<em>Keywords: statement, length, reason, proof</em>
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Answer:
Ur answer will be B.
Step-by-step explanation:
A dilation will always create an image smaller or bigger than the pre-image making it not congruent since it changes in size.
