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Help on math? :)

If the angle formed by the tangent satellite signals is 138 degrees, what is the measure of the intercepted arc on Earth?


The farthest distance a satellite signal can directly reach is the length of the segment tangent (l to the curve of Earth's surface. The diagram is not drawn to scale.


A. 84 degrees

B. 276 degrees

C. 42 degrees

D. 69 degrees

Help on math If the angle formed by the tangent satellite signals is 138 degrees what is the measure of the intercepted arc on Earth The farthest distance a sat class=

Respuesta :

1. Let O be the center of the sphere, A the tangency point and B the location of the satellite. (as in the figure below)

2. Join B to O. M(ABO)=[tex] \frac{1}{2} [/tex]m(B)=(1/2)*138°=69°.


3. m(OAB)=90° as a radius to a tangency point is perpendicular to the tangent at that point. 

4. m(AOB)=180°-90°-69°=21°.

5. check picture 2. Arc AM is equal to the measure of the central angle AOM = 21°.

6. The measure of the intercepted arc is 21°*2=42°
Ver imagen eco92
Ver imagen eco92
akposevictor

Using the central angle theorem, the measure of the intercepted arc on Earth is: 42°

What is the Central Angle Theorem?

Based on the central angle theorem, the measure of a central angle equals the measure of the intercepted arc.

Half of the measure of the central angle = 180 - 90 - 138/2 = 21°

Central angle = 42°

Central angle = intercepted arc

Intercepted arc = 42°

Learn more about the central angle theorem on:

https://brainly.com/question/5436956

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