Kapil is programming a robot to always know its distance from its charging base by following these steps

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Kapil is programming a robot to always know its distance from its charging base by following these steps

Step 1) save b, which is the current distance from the base

Step 2) Face charging base and turn α° to the right

Step 3) Move x  

Step 4) Compute new distance from the base  

Step 5) Go back to Step 1  

For example, it might happen that when the robot gets to step 4 in its program  

b = 70 units

α = 60°, and

x = 50 units

In the example above, what would the robot's new distance from its base be?

The robot's new distance from its base is 62

Step-by-step explanation:

Look to the attached figure

To find the robot's new distance from its base let us use the cosine rule

b, x and the robot's new distance from its base formed a triangle, where b = 70 , x = 50 and the angle between them α = 60°

Assume that the robot's new distance from its base is z

∵ The formula of cosine rule is

∵ x = 50

∵ b = 70

∵ α = 60°

- Substitute them in the formula above

∴  

∴  

∴  

∴  

∴ z = 62.44997998

- Round it to the nearest unit

∴ z = 62

∵ z represents the robot's new distance from its base

∴ The robot's new distance from its base is 62

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step-by-step explanation: