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JL is a common tangent to circles M and K at point J. If angle MLK measures
619, what is the length of radius MJ? Round to the nearest hundredth. (Hint:
Show that triangles LMJ and LKJ are right triangles, and then use right triangle
trigonometry to solving for missing sides of the right triangles.) (10 points)

pls help

JL is a common tangent to circles M and K at point J If angle MLK measures 619 what is the length of radius MJ Round to the nearest hundredth Hint Show that tri class=

Respuesta :

thebecks

Answer:

MJ = 6.5

Step-by-step explanation:

Tangent lines to a circle are perpendicular to the radius.

tan 68° = JL/3

2.4751 = JL/3

JL = 7.4253

∠JLK = 90° - 68° = 22°

∠MLJ = 61° - 22° = 39°

sin 61° = MJ/7.4253

MJ = 7.4253(0.8746) =  6.5

MrRoyal

The length of radius MJ is 5.99 units

How to calculate the radius MJ?

Start by calculating the length JL using the following tangent ratio

tan(68°) = JL/3

Make JL the subject

JL = 3 * tan(68°)

Evaluate the product

JL = 7.4

From the figure, the measure of angle MLJ is:

∠MLJ = MLK - JLK

Where:

∠JLK = 90° - 68° = 22°

So, we have:

∠MLJ = 61 - 22

∠MLJ = 39

The radius MJ is then calculated using the following tangent ratio

tan(39) = MJ/JL

This gives

tan(39) = MJ/7.4

Make MJ the subject

MJ = 7.4 * tan(39)

Evaluate

MJ = 5.99

Hence, the length of radius MJ is 5.99 units

Read more about line of tangents at:

https://brainly.com/question/6617153

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