Answer:
Option D is correct.
Step-by-step explanation:
Given,
In ΔABC, ∠A = 42° , ∠B = 56° & a = 7
We use law of sines,
which has following expression:
![\frac{a}{sin\,A}=\frac{b}{sin\,B}\frac{c}{sin\,C}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bsin%5C%2CA%7D%3D%5Cfrac%7Bb%7D%7Bsin%5C%2CB%7D%5Cfrac%7Bc%7D%7Bsin%5C%2CC%7D)
First we find value of ∠C
∠A + ∠B + ∠C = 180° (Angle Sum Property of Triangle)
42 + 56 + ∠C = 180
∠C = 180 - 98
∠C = 82°
Now using law of sines, we get
![\frac{7}{sin\,42}=\frac{b}{sin\,56}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7Bsin%5C%2C42%7D%3D%5Cfrac%7Bb%7D%7Bsin%5C%2C56%7D)
![\frac{7}{0.67}=\frac{b}{0.83}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B0.67%7D%3D%5Cfrac%7Bb%7D%7B0.83%7D)
![b=\frac{7}{0.67}\times0.83](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B7%7D%7B0.67%7D%5Ctimes0.83)
![b=8.67](https://tex.z-dn.net/?f=b%3D8.67)
![\frac{7}{sin\,42}=\frac{c}{sin\,82}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7Bsin%5C%2C42%7D%3D%5Cfrac%7Bc%7D%7Bsin%5C%2C82%7D)
![\frac{7}{0.67}=\frac{c}{0.99}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B0.67%7D%3D%5Cfrac%7Bc%7D%7B0.99%7D)
![c=\frac{7}{0.67}\times0.99](https://tex.z-dn.net/?f=c%3D%5Cfrac%7B7%7D%7B0.67%7D%5Ctimes0.99)
![c=10.36](https://tex.z-dn.net/?f=c%3D10.36)
Therefore, Option D is correct.
Answer:
The total area of the figure is ![22.5\ in^{2}](https://tex.z-dn.net/?f=22.5%5C%20in%5E%7B2%7D)
Step-by-step explanation:
we know that
The area of the figure is equal to the area of the rectangle plus the area of the isosceles right triangle
<u>Find the area of rectangle</u>
![A=(6)(3)=18\ in^{2}](https://tex.z-dn.net/?f=A%3D%286%29%283%29%3D18%5C%20in%5E%7B2%7D)
Find the area of the isosceles right triangle
![A=\frac{1}{2}(3)(3)=4.5\ in^{2}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%283%29%283%29%3D4.5%5C%20in%5E%7B2%7D)
<u>Find the total area of the figure</u>
![18\ in^{2}+4.5\ in^{2}=22.5\ in^{2}](https://tex.z-dn.net/?f=18%5C%20in%5E%7B2%7D%2B4.5%5C%20in%5E%7B2%7D%3D22.5%5C%20in%5E%7B2%7D)
Answer:
I'm not completely sure about the first one, but #8 is 0.0419, and #9 is 30500.
Answer:
$27.32
Step-by-step explanation:
25.30 x.08= 2.02
add 2.02 to 25.30 =
$27.32
Answer:
17 3.14
/30
Step-by-step explanation: