Answer:
D. m∠A=43, m∠B=55, a=20
Step-by-step explanation:
Given:
∆ABC,
m<C = 82°
AB = c = 29
AC = b = 24
Required:
m<A, m<C, and a (BC)
SOLUTION:
Find m<B using the law of sines:
![\frac{sin(B)}{b} = \frac{sin(C)}{c}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bsin%28B%29%7D%7Bb%7D%20%3D%20%5Cfrac%7Bsin%28C%29%7D%7Bc%7D%20)
![\frac{sin(B)}{24} = \frac{sin(82)}{29}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bsin%28B%29%7D%7B24%7D%20%3D%20%5Cfrac%7Bsin%2882%29%7D%7B29%7D%20)
![sin(B)*29 = sin(82)*24](https://tex.z-dn.net/?f=%20sin%28B%29%2A29%20%3D%20sin%2882%29%2A24%20)
![\frac{sin(B)*29}{29} = \frac{sin(82)*24}{29}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bsin%28B%29%2A29%7D%7B29%7D%20%3D%20%5Cfrac%7Bsin%2882%29%2A24%7D%7B29%7D%20)
![sin(B) = \frac{sin(82)*24}{29}](https://tex.z-dn.net/?f=%20sin%28B%29%20%3D%20%5Cfrac%7Bsin%2882%29%2A24%7D%7B29%7D%20)
![sin(B) = 0.8195](https://tex.z-dn.net/?f=%20sin%28B%29%20%3D%200.8195%20)
![B = sin^{-1}(0.8195)](https://tex.z-dn.net/?f=%20B%20%3D%20sin%5E%7B-1%7D%280.8195%29%20)
![B = 55.0](https://tex.z-dn.net/?f=%20B%20%3D%2055.0%20)
m<B = 55°
Find m<A:
m<A = 180 - (82 + 55) => sum of angles in a triangle.
= 180 - 137
m<A = 43°
Find a using the law of sines:
![\frac{a}{sin(A)} = \frac{b}{sin(B)}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%7D%7Bsin%28A%29%7D%20%3D%20%5Cfrac%7Bb%7D%7Bsin%28B%29%7D%20)
![\frac{a}{sin(43)43} = \frac{24}{sin(55)}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%7D%7Bsin%2843%2943%7D%20%3D%20%5Cfrac%7B24%7D%7Bsin%2855%29%7D%20)
Cross multiply
![a*sin(55) = 25*sin(43)](https://tex.z-dn.net/?f=%20%20a%2Asin%2855%29%20%3D%2025%2Asin%2843%29%20)
![a = \frac{25*sin(43)}{sin(53)}](https://tex.z-dn.net/?f=%20%20a%20%3D%20%5Cfrac%7B25%2Asin%2843%29%7D%7Bsin%2853%29%7D%20)
(approximated)
Answer: 0.44 qtr
Step-by-step explanation:
10 centimeters to quarters = 0.44 qtr
<em>☽------------❀-------------☾</em>
<em>Hi there!</em>
<em>~</em>
<em>Answer:</em>
<em>2 must be the no. by which 3456 must be divided so that the quotient becomes a perfect cube.</em>
<em>❀Hope this helped you!❀</em>
<em>☽------------❀-------------☾</em>
<em></em>
Answer:
A. 16c - 3
Step-by-step explanation:
You simply add the two expressions for Saturday and Sunday. 6c+9+10c-12= 16c-3.