construct a triangle XYZ in which |YZ|=6 cm angle XYZ=60° and |XZ|=9 cm measure|XY| , construct a mediator of XY and draw a circle with center X and a radius of 5cm. Measure|YA|, where A is the point of intersection of the mediator and the circle in the triangular region XYZ
I want in figure
sin60°/9 = sinX/6
X = 35.3°
So, Z = 84.7°
XY/sin84.7° = 9/sin60°
XY = 10.35
not sure what a mediator XY is
you mean the median from Z to XY?
Since XY is just about exactly 10, the circle will touch XY pretty much at its center.
Maybe a bit of explanation is in order. Or maybe, knowing all the sides, you can finish up yourself.
Show me the answers and construction please
Armah
To construct triangle XYZ, follow these steps:
1. Start by drawing a line segment XY of any convenient length. Let's say XY is 5 cm.
2. Construct an angle of 60 degrees at point X. To do this, use a protractor to measure an angle of 60 degrees starting from line segment XY.
3. With X as the center, draw an arc with a radius of 9 cm to intersect the angle's sides. Let's label this point of intersection as Z.
4. Draw a line segment YZ connecting points Y and Z. The length of YZ is given as 6 cm.
Now, to construct the mediator of XY:
5. Locate the midpoint M of line segment XY. To do this, use a ruler to measure the halfway point between X and Y.
6. Draw a line passing through M and perpendicular to XY. This line is the mediator of XY and will intersect XY at point A.
To draw a circle with center X and a radius of 5 cm:
7. Using X as the center, draw an arc with a radius of 5 cm. This arc should intersect XY at point A.
8. Label the point of intersection between the mediator and the circle as A.
To measure the length of YA:
9. Use a ruler to measure the distance between points Y and A. This will give you the length of YA.