Answer:
R= 20.88 ft
Step-by-step explanation:
See the diagram attached, this satisfies the condition, ΔKLM is enclosed in a circle of radius R.
LN=16 ft (given)
The value of KM is 2R because as the ∠KLM forms an angle of 90°, therefore, the line KM passes through the center.
Area of a triangle = [tex]\frac{1}{2} * Base * Height[/tex]
Now let's find he area of the ΔKLM=[tex]\frac{1}{2} * KM * LN[/tex]
= [tex]\frac{1}{2} * 2R* 16\\\\=16R[/tex]
Also the area can be found out by =[tex]\frac{1}{2} * KL*LM[/tex]( As KLM is a right angled triangle)
KL= KM cos 25°= 2R cos 25°
LM= KM cos 55°= 2R sin 25°
Area= [tex]\frac{1}{2}[/tex] x 2R cos 25°x 2R sin 25 °
= [tex]R^{2}[/tex] sin 50°
[tex]R^{2}[/tex] sin 50°= 16R
R sin 50°=16
R= 20.88 ft
