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For the final exam in a scuba diving certification course, Karl naviga
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09 Jun 2023, 07:44
09 Jun 2023, 07:44
Expert Reply
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Question Stats:
87% (01:52) correct
12% (05:16) wrong based on 8 sessions
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For the final exam in a scuba diving certification course, Karl navigates from one point in a lake to another. Karl begins the test x meters directly beneath the boat and swims straight down toward the bottom of the lake for 8 meters. He then turns to his right and swims in a straight line parallel to the surface of the lake and swims 24 meters, at which point he swims directly from his location, in a straight line, back to the boat. If the distance that Karl swims back to the boat is 26 meters, what is the value of x ?
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Re: For the final exam in a scuba diving certification course, Karl naviga
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10 Jun 2023, 04:04
10 Jun 2023, 04:04
2
(x+8)^2 + 24^2 = 26^2
(x+8)^2 = 100
x = 2
(x+8)^2 = 100
x = 2
Re: For the final exam in a scuba diving certification course, Karl naviga
[#permalink]
11 Jun 2023, 04:00
11 Jun 2023, 04:00
Expert Reply
OE
Draw a diagram. The question states that Karl started x meters below the boat and then swam 8 meters straight down, which puts Karl x + 8 meters below the boat. Karl makes a right turn and swims parallel to the water 24 meters. He then swims 26 meters directly back to the boat. This completes a right triangle with a hypotenuse of 26 meters and legs of 24 and x + 8 meters. Use the Pythagorean Theorem to show that 10^2 meters + 24^2 meters = 26^2 meters. So, this is a 10-24-26 triangle, which is twice the sides of a familiar 5-12-13 triangle. The question asks for the value of x, the number of meters below the boat that Karl began his dive from, which is found by the equation x + 8 = 10, so x = 2.
Draw a diagram. The question states that Karl started x meters below the boat and then swam 8 meters straight down, which puts Karl x + 8 meters below the boat. Karl makes a right turn and swims parallel to the water 24 meters. He then swims 26 meters directly back to the boat. This completes a right triangle with a hypotenuse of 26 meters and legs of 24 and x + 8 meters. Use the Pythagorean Theorem to show that 10^2 meters + 24^2 meters = 26^2 meters. So, this is a 10-24-26 triangle, which is twice the sides of a familiar 5-12-13 triangle. The question asks for the value of x, the number of meters below the boat that Karl began his dive from, which is found by the equation x + 8 = 10, so x = 2.
