Answer:
The other angle is 33
Step-by-step explanation:
Complementary angles add to 90
57+x = 90
subtract 57 from each side
x = 90-57
x = 33
Answer:
3 / 4
Step-by-step explanation:
The original no. = x / x + 10 [ Numerator is taken as x ]
The new no. = x + 19 / (x + 10) - 1
= x + 19 / x + 9 = 3 / 2
Equation-
x + 19 / x + 9 = 3 / 2
By cross multiplying, we get,
2x + 38 = 3x + 27
2x - 3x = 27 - 38
-x = -11
x = 11
Therefore the original no. = ( 11 + 19 ) / ( 11 + 19 + 10 )
= 30 / 40
= 3 / 4
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Answer:
x = -48
Step-by-step explanation:
4x + 2 = 5(x + 10)
expand the 5(x+10)
4x + 2 = 5x + 50
-2 both sides
4x + 2 - 2 = 5x + 50 - 2
simplify
4x = 5x + 48
-5x both sides
4x - 5x = 5x + 48 - 5x
simplify
-x = 48
÷ (-1) both sides
-x ÷ (-1) = 48 ÷ (-1)
simplify
x = -48
The answer is x = -48.
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>
<h2>Hello There today we will solve your problem</h2>
<em>Response-</em>
<em>ABC is absolutely a right triangle</em>
<em>we can use the pythagorean theorem to solve this</em>
<h3><em>Definitions</em></h3>
Right Triangle - <em>A right triangle or right-angled triangle, or more formally an orthogonal triangle, is a triangle in which one angle is a right angle. The relation between the sides and other angles of the right triangle is the basis for trigonometry. The side opposite to the right angle is called the hypotenuse.</em>
Pythagorean Theorem - <em>In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.</em>
<em>_________________</em>
<em>To use to the Pythagorean Theorem it is</em>
![A^2+B^2=C^2](https://tex.z-dn.net/?f=A%5E2%2BB%5E2%3DC%5E2)
For our equation
would be
would be ![5](https://tex.z-dn.net/?f=5)
<em>_________________</em>
<h2><em>Solve</em></h2>
![12^2+5^2\\144+25\\169\\C^2=169\\C=13](https://tex.z-dn.net/?f=12%5E2%2B5%5E2%5C%5C144%2B25%5C%5C169%5C%5CC%5E2%3D169%5C%5CC%3D13)
Since we got
this is a right triangle since it's what we had before.