Answer:
x =20.8
Step-by-step explanation:
We can find the value of 1/2 of x using the Pythagorean theorem
a^2 + b^2 = c^2
a^2 + 6^2 = 12^2
a^2 = 36+144
a^2 = 108
Take the square root
sqrt(a^2) = sqrt( 108)
a =sqrt(36*3)
a = sqrt(36) sqrt(3)
a = 6sqrt(3)
Now x = 2 times the length of a
x = 2 * 6 sqrt(3)
x = 12 sqrt(3)
x =20.78460969
x =20.8
Let the medium angle be B degrees
the small angle be A degrees
the large angle be C degrees
Then
C = 2 B + 20 ..................X
5 B = A + C ..................Y
Sum of all angles
A + B + C = 180 .............Z
Applying Y in Z
5 B + B = 180
6 B = 180
B = 30
From X C = 2 x 30 + 20 = 60 + 20 = 80
From Y 5 x 30 = A + 80
150 = A + 80
150 - 80 = A = 70
Hence medium angle B = 30 degrees
the small angle A = 70 degrees
the large angle C = 80 degrees
Two triangle are congruent when the shape and size of both the triangle are same. The given information is the SAS case.
To find the form of the case we need to know about the triangle congruence theorem.
<h3>What is triangle congruence theorem?</h3>
Two triangle are congruent when the shape and size of both the triangle are same.
Triangle congruence theorem are-
- Angle-Side-Angle theorem (AAS)- This theorem states that two triangle is congruent when two angle and one side of the triangle are respectively equal to the two angles and same side of the other triangle.
- Side-Side-Side theorem (SSS)- When the three sides of the one triangle is equal to the three sides of the other triangle respectively, then the triangle are congruent.
- Side-Angle-Side theorem (SAS)- Two sides and the included angle of are equal to the two sides and one angle of other triangle respectively.
Given information-
Evelyn is 104 meters from the take off.
The angle of elevation of the plane is 12°.
The plane is 100 meters away from the takeoff point.
The distance is 100 meters and 104 meters. The other two sides , as are same and the angle of elevation is also same for this case (12 degrees).
Thus the two triangle formed which are congruent.
As above discussed the case of SAS exists for the triangle congruence theorem.
Hence the given information is the SAS case.
Learn more about the triangle congruence theorem here;
brainly.com/question/19258025
The upper quartile for the data set given below is. 14, 8, 23, 9, 11, 27, 22, 3, 17, 12, 29
LekaFEV [45]
Ok, first we need to organize.
<span>14, 8, 23, 9, 11, 27, 22, 3, 17, 12, 29
</span>3, 8, 9, 11, 12, 14, 17, 22, 23, 27, 29.
First, we need to find the median, the or the middle, which is 14.
Now that we know the median is fourteen, we take away all numbers to the left of 14, including 14: 17, 22, 23, 27, 29. Now just find the median in this new set of numbers. This will give us our upper quartile, which is 23. Hope this helped, and don't forget to drop a like.
Answer:
150:120
Step-by-step explanation:
U add the 2 ratios 5+4=9
270/9=30
30*5=150
30*4=120