Answer:
Side CA = 7.8
Step-by-step explanation:
<u>Given:</u>
Acute angled
.
![\angle B =40^\circ](https://tex.z-dn.net/?f=%5Cangle%20B%20%3D40%5E%5Ccirc)
AB = 10
BC = 12
We can use cosine rule here to find the side AC = b
<em>Formula for cosine rule:
</em>
![cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}](https://tex.z-dn.net/?f=cos%20B%20%3D%20%5Cdfrac%7Ba%5E%7B2%7D%2Bc%5E%7B2%7D-b%5E%7B2%7D%7D%7B2ac%7D)
Where
a is the side opposite to ![\angle A](https://tex.z-dn.net/?f=%5Cangle%20A)
b is the side opposite to ![\angle B](https://tex.z-dn.net/?f=%5Cangle%20B)
c is the side opposite to ![\angle C](https://tex.z-dn.net/?f=%5Cangle%20C)
![cos 40 = \dfrac{12^{2}+10^{2}-b^{2}}{2\times 12\times 10}\\\Rightarrow cos 40 = \dfrac{144+100-b^{2}}{240}\\\Rightarrow 0.77 = \dfrac{244-b^{2}}{240}\\\Rightarrow 244-b^{2} = 0.77 \times 240\\\Rightarrow 244-b^{2} = 183.85\\\Rightarrow 244-183.85 = b^{2}\\\Rightarrow b^2 = 60.15\\\Rightarrow b = 7.76](https://tex.z-dn.net/?f=cos%2040%20%3D%20%5Cdfrac%7B12%5E%7B2%7D%2B10%5E%7B2%7D-b%5E%7B2%7D%7D%7B2%5Ctimes%2012%5Ctimes%2010%7D%5C%5C%5CRightarrow%20cos%2040%20%3D%20%5Cdfrac%7B144%2B100-b%5E%7B2%7D%7D%7B240%7D%5C%5C%5CRightarrow%200.77%20%3D%20%5Cdfrac%7B244-b%5E%7B2%7D%7D%7B240%7D%5C%5C%5CRightarrow%20244-b%5E%7B2%7D%20%3D%200.77%20%5Ctimes%20240%5C%5C%5CRightarrow%20244-b%5E%7B2%7D%20%3D%20183.85%5C%5C%5CRightarrow%20244-183.85%20%3D%20b%5E%7B2%7D%5C%5C%5CRightarrow%20b%5E2%20%3D%2060.15%5C%5C%5CRightarrow%20b%20%3D%207.76)
To the nearest tenth <em>b = 7.8</em>
<u>Answer:</u>
9. x = 12
10. x = 31
<u>Step-by-step explanation:</u>
9. Corresponding angles are equal, so technically you can move that (7x - 20) to be diagonal with the (4x + 16). Along with the corresponding angle, diagonal angles are equal to each other. Therefore you can set (7x - 20) equal to (4x + 16) to find x.
7x - 20 = 4x + 16
Solve
3x - 20 = 16
3x = 36
x = 12
Therefore x is equal to 12
<u>Check:</u>
4(12) + 16
= 64
7(12) - 20
= 64
10. All angles in a triangle have to add up to 180 degrees. Therefore, you can write your equation like this:
x + 2x + 25 + 2x = 180
Combine like terms
5x + 25 = 180
Solve
5x = 155
x = 31
Therefore, x = 31.
<u>Check:</u>
31 + 2(31) + 25 + 2(31) = 180
31 + 62 + 25 + 62 = 180
180 = 180
<em>I hope this helps!!</em>
<em>- Kay :)</em>
<em />
<span>The side opposite the 30 degree angle is half of the hypotenuse.
a^2 + b^2 = c^2 =>
a^2 + (c/2)^2 = c^2
12^2 + c^2/4 = c^2
4*12^2 + c^2 - 4c^2 = 0
576 - 3c^2 = 0
- 3c^2 = - 576
c^2 = 192
c = 8√3
</span>