A gecko is in a room that is 12 feet long, 10 feet wide and 8 feet tall. The gecko is currently on a side wall ($10^{\prime}$ by
$8^{\prime}$), one foot from the ceiling and one foot from the back wall ($12^{\prime}$ by $8^{\prime}$). The gecko spots a fly on the opposite side wall, one foot from the floor and one foot from the front wall. What is the length of the shortest path the gecko can take to reach the fly assuming that it does not jump and can only walk across the ceiling and the walls?
1 answer:
Answer: The shortest is 22.4 feet
Step-by-step explanation: For the gecko to walk the shortest distance, it has to go straight from where it is to the celling, diagonally from the celling to the wall where the fly is and straight from the corner of the celling to where the fly is.
straight from where it is to the celling: 1 feet
diagonally from the celling to the wall where the fly:
it is a right triangle hipotenuse what we want, leg 12 and 8. (see picture attached): h² = 12² + 8² h = √208 h = 14.4 feet
straight from the corner of the celling to where the fly is: 7 feet.
1 + 14.4 + 7 = 22.4
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M∠X = 54.3°.
Using the Law of Sines, we have:
Cross multiplying gives us
61(sin 34) = 42(sin X)
Divide both sides by 42:
(61(sin 34))/42 = (42(sin X))/42
(61(sin 34))/42 = sin X
Take the inverse sine of both sides:
sin⁻¹((61(sin 34))/42) = sin⁻¹(sin X)
54.3 = X
Using the Law of Sines, we have:
Cross multiplying gives us
61(sin 34) = 42(sin X)
Divide both sides by 42:
(61(sin 34))/42 = (42(sin X))/42
(61(sin 34))/42 = sin X
Take the inverse sine of both sides:
sin⁻¹((61(sin 34))/42) = sin⁻¹(sin X)
54.3 = X