Question

Given: LN ⊥ KM LN = 16 ft m∠K = 25°, m∠M = 55° Find: Radius R

Answer 1

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 = $\frac{1}{2} * Base * Height$

Now let's find he area of the ΔKLM=$\frac{1}{2} * KM * LN$

                                                          = $\frac{1}{2} * 2R* 16\\\\=16R$

Also the area can be found out by =$\frac{1}{2} * KL*LM$( As KLM is a right angled triangle)

KL= KM cos 25°= 2R cos 25°

LM= KM cos 55°= 2R sin 25°

Area= $\frac{1}{2}$ x 2R cos 25°x 2R sin 25 °

      = $R^{2}$ sin 50°

$R^{2}$ sin 50°= 16R

R sin 50°=16

R= 20.88 ft