Answer:
98
Step-by-step explanation:
From the statement of similarity, we can write this proportion.
TV/MV = UV/LV
28/x = 16/56
16x = 28 × 56
x = 7 × 14
x = 98
Answer:
15/4
Step-by-step explanation:
The formula for slope is:
(y₂-y₁)/(x₂-x₁)
Now we plug in the coordinates given to us into the equation:
(5-(-10))/(-1-(-5))
15/4
Answer:
Yea it does
Step-by-step explanation:
<span>(3.5, 3) is the circumcenter of triangle ABC.
The circumcenter of a triangle is the intersection of the perpendicular bisectors of each side. All three of these perpendicular bisectors will intersect at the same point. So you have a nice self check to make sure your math is correct. Now let's calculate the equation for these bisectors.
Line segment AB:
Slope
(4-2)/(1-1) = 2/0 = infinity.
This line segment is perfectly vertical. So the bisector will be perfectly horizontal, and will pass through ((1+1)/2, (4+2)/2) = (2/2, 6/2) = (1,3).
So the equation for this perpendicular bisector is y = 3.
Line segment BC
(2-2)/(6-1) = 0/5 = 0
This line segment is perfectly horizontal. So the bisector will be perfectly vertical, and will pass through ((1+6)/2,(2+2)/2) = (7/2, 4/2) = (3.5, 2)
So the equation for this perpendicular bisector is x=3.5
So those two bisectors will intersect at point (3.5,3) which is the circumcenter of triangle ABC.
Now let's do a cross check to make sure that's correct.
Line segment AC
Slope = (4-2)/(1-6) = 2/-5 = -2/5
The perpendicular will have slope 5/2 = 2.5. So the equation is of the form
y = 2.5*x + b
And will pass through the point
((1+6)/2, (4+2)/2) = (7/2, 6/2) = (3.5, 3)
Plug in those coordinates and calculate b.
y = 2.5x + b
3 = 2.5*3.5 + b
3 = 8.75 + b
-5.75 = b
So the equation for the 3rd bisector is
y = 2.5x - 5.75
Now let's check if the intersection with this line against the other 2 works.
Determining intersection between bisector of AC and AB
y = 2.5x - 5.75
y = 3
3 = 2.5x - 5.75
8.75 = 2.5x
3.5 = x
And we get the correct value. Now to check AC and BC
y = 2.5x - 5.75
x = 3.5
y = 2.5*3.5 - 5.75
y = 8.75 - 5.75
y = 3
And we still get the correct intersection.</span>
Answer:
50 degrees
Step-by-step explanation:
Okay! So first off, because this is NOT a right triangle, we can't use soh cah toa. That means we can either use the law of sines or the law of cosines.
Because we only have sides here and no angles, we are forced to use the law of cosines.
c^2 = a^2 + b^2 − 2ab cos(C)
c = 6
b = 7.5
a = 6.5
36 = 6.5^2 + 7.5^2 - 2(6.5)(7.5)cos(C)
36 = 98.5 - 97.5cos(C)
-62.5 = -97.5cos(C)
0.641 = cos(C)
angle C = cos^-1(0.641)
angle C = 50.13 which is around 50 degrees
Remember! A dumb thing i always used to do in geometry was use radians instead of degrees, be sure to use degrees here because you are looking for degrees. Radians are for things involving not degrees, but PI.
