It is a percent decrease because the original is less than the final value and the answer is -24% decrease. Please give me brainless if right.
Answer:
Angle A = Angle Y
Angle B = Angle Z
Angle C = Angle X
AB = YZ
AC = YX
BC = ZX
Triangle ABC = Triangle YZX
Step-by-step explanation:
Find this by looking at the corresponding parts on the other triangle. They have the same marking on them. Make sure that when answering for segments or triangles that the order is the same on both sides.
<u>Part 1) </u>To find the measure of ∠A in ∆ABC, use
we know that
In the triangle ABC
Applying the law of sines
![\frac{a}{sin\ A}=\frac{b}{sin\ B}=\frac{c}{sin\ C}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bsin%5C%20A%7D%3D%5Cfrac%7Bb%7D%7Bsin%5C%20B%7D%3D%5Cfrac%7Bc%7D%7Bsin%5C%20C%7D)
in this problem we have
![\frac{a}{sin\ A}=\frac{b}{sin\ theta}\\ \\a*sin\ theta=b*sin\ A\\ \\ sin\ A=\frac{a*sin\ theta}{b} \\ \\ A=arc\ sin (\frac{a*sin\ theta}{b})](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bsin%5C%20A%7D%3D%5Cfrac%7Bb%7D%7Bsin%5C%20theta%7D%5C%5C%20%5C%5Ca%2Asin%5C%20theta%3Db%2Asin%5C%20A%5C%5C%20%5C%5C%20sin%5C%20A%3D%5Cfrac%7Ba%2Asin%5C%20theta%7D%7Bb%7D%20%5C%5C%20%5C%5C%20A%3Darc%5C%20sin%20%28%5Cfrac%7Ba%2Asin%5C%20theta%7D%7Bb%7D%29)
therefore
<u>the answer Part 1) is</u>
Law of Sines
<u>Part 2) </u>To find the length of side HI in ∆HIG, use
we know that
In the triangle HIG
Applying the law of cosines
![g^{2}=h^{2}+i^{2}-2*h*i*cos\ G](https://tex.z-dn.net/?f=g%5E%7B2%7D%3Dh%5E%7B2%7D%2Bi%5E%7B2%7D-2%2Ah%2Ai%2Acos%5C%20G)
In this problem we have
g=HI
G=angle Beta
substitute
![HI^{2}=h^{2}+i^{2}-2*h*i*cos\ Beta](https://tex.z-dn.net/?f=HI%5E%7B2%7D%3Dh%5E%7B2%7D%2Bi%5E%7B2%7D-2%2Ah%2Ai%2Acos%5C%20Beta)
![HI=\sqrt{h^{2}+i^{2}-2*h*i*cos\ Beta}](https://tex.z-dn.net/?f=HI%3D%5Csqrt%7Bh%5E%7B2%7D%2Bi%5E%7B2%7D-2%2Ah%2Ai%2Acos%5C%20Beta%7D)
therefore
<u>the answer Part 2) is</u>
Law of Cosines
Answer:
c. 45d+.25m
Step-by-step explanation: