Respuesta :

First of all, tangents make an angle of 90 degrees with the radius of a circle.

Hence, Both the triangles are right angled.

Now apply pythagorean theorem on triangle LKJ, and find the length of tangent,

which is x= tan(68) * 3 = 7.42

Now, on LMJ to find MJ

so, MJ = 7.42 * tan(61) = 13.39

Hope it helps

The length of radius MJ exists at 5.99 units.

How to calculate the radius MJ?

Given:

JL is a common tangent to circles M and K at point J.

If angle MLK measures 619.

Calculating the length JL utilizing the following tangent ratio.

tan(68°) = JL/3

Simplifying the above equation, we get

JL = 3 [tex]*[/tex] tan(68°)

JL = 7.4

From the figure, the measure of angle MLJ exists:

∠MLJ = MLK - JLK

Where:

∠JLK = 90° - 68° = 22°

We have:

∠MLJ = 61° - 22°

∠MLJ = 39°

The radius MJ exists then estimated utilizing the following tangent ratio

tan(39) = MJ/JL

tan(39) = MJ/7.4

Simplifying the above equation,

[tex]MJ = 7.4 * tan(39)[/tex]

Evaluating,

MJ = 5.99

Hence, the length of radius MJ exists at 5.99 units.

To learn more about calculating the radius

https://brainly.com/question/23025496

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