construct triangle jkl with JK 8 cm kl-6 cm and angle J K L is 60 degrees. draw a circle touching the edges. what is the radius of the circle?
Jkl has jk=10cm,Jl=
Triangle IJK such that IJ=JK=8cm and JKI=60o.draw
4.6
4.6cm
To construct triangle JKL, follow these steps:
1. Draw a line segment JK of length 8 cm.
2. From point J, draw an arc with a radius of 6 cm.
3. From point K, draw an arc with a radius of 8 cm.
4. Label the points of intersection between the arcs as L.
You have now constructed triangle JKL with JK = 8 cm, KL = 6 cm, and angle JKL measuring 60 degrees.
To draw a circle touching the edges of triangle JKL, follow these steps:
1. Find the incenter of triangle JKL. The incenter is the point where the angle bisectors of the triangle intersect. Use a compass to find this point.
2. Place the compass needle on the incenter and adjust the radius of the compass to match the distance between the incenter and one of the sides of the triangle, such as JK.
3. With the compass set, draw a circle that touches all three sides of the triangle.
To find the radius of the circle, you can use the formula for the inradius of a triangle. The inradius can be calculated using the following formula:
inradius = Area of the triangle / Semiperimeter of the triangle
The semiperimeter of triangle JKL can be calculated by adding the lengths of its sides and dividing by 2:
Semiperimeter = (JK + KL + LJ) / 2
The area of triangle JKL can be calculated using the Heron's formula:
Area = √(s(s-JK)(s-KL)(s-LJ))
Where s is the semiperimeter.
Once you have the area and semiperimeter, you can calculate the radius of the circle using the formula above.
draw JK of length 8
construct a 60° angle at K, and extend the side
mark off KL = 6 and label L. Close the triangle
Now bisect two of the angles. The bisectors intersect at the circumcenter.
Draw the circle, and then calculate the radius.
google can help you with any of these steps, if necessary.