The question is incomplete, the complete question is here
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?
Answer:
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 [tex]z=\sqrt{x^{2}+b^{2}-2(x)(b)(cos\alpha })[/tex]
∵ x = 50
∵ b = 70
∵ α = 60°
- Substitute them in the formula above
∴ [tex]z=\sqrt{(50)^{2}+(70)^{2}-2(50)(70)(cos60)[/tex]
∴ [tex]z=\sqrt{2500+4900-7000(0.5)}[/tex]
∴ [tex]z=\sqrt{2500+4900-3500}[/tex]
∴ [tex]z=\sqrt{3900}[/tex]
∴ 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
