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What is the length of hypotenuse K?
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Updated on: 12 Apr 2019, 11:25
Updated on: 12 Apr 2019, 11:25
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Question Stats:
62% (02:55) correct
37% (02:31) wrong based on 32 sessions
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What is the length of hypotenuse K?
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7.8
Re: Find the length of hypotenuse K
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12 Apr 2019, 21:07
12 Apr 2019, 21:07
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LT2018 wrote:
Any more explanations for this question?
Plz see the diag. below
As
Now the left hand triangle is a 5-12-13 triangle (Pythagorean triplet) ( it can also be derived by Pythagoras theorem as the unknown side = \(\sqrt{13^2 - 12^2} = 5\)
Since the left part of the triangle has got the base 5, hence the base of the other triangle = 12.2 - 5 = 7.2
Now both triangles are similar ( Angle - angle -angle)
and hence the side can be deduced in the form:
\(\frac{7.2}{12}= \frac{k}{13}\)
or \(k = 7.8\)
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Re: What is the length of hypotenuse K?
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11 Jun 2021, 22:39
11 Jun 2021, 22:39
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Begin by noting that the triangle on the left is a 5–12–13 Pythagorean
triple, so the bottom side is 5. Subtract 12.2 – 5 = 7.2 to get the bottom side of
the triangle on the right.
Next, the two unmarked angles that “touch” at the middle must sum to 90°,
because they form a straight line together with the right angle of 90° between
them, and all three angles must sum to 180°. Mark the angle on the left x. The
angle on the right must then be 90 – x.
Now the other angles that are still unmarked can be labeled in terms of x.
Using the rule that the angles in a triangle sum to 180°, the angle between 12
and 13 must be 90 – x, while the last angle on the right must be x,
Since each triangle has angles of 90, x, and 90 – x, the triangles are similar.
This observation is the key to the problem. Now you can make a proportion,
carefully tracking which side corresponds to which. The 7.2 corresponds to
12, since each side is across from angle x. Likewise, k corresponds to 13,
since each side is the hypotenuse. Write the equation and solve for k:
7.2/12=k/13
k=13*7.2/12
k=7.8
triple, so the bottom side is 5. Subtract 12.2 – 5 = 7.2 to get the bottom side of
the triangle on the right.
Next, the two unmarked angles that “touch” at the middle must sum to 90°,
because they form a straight line together with the right angle of 90° between
them, and all three angles must sum to 180°. Mark the angle on the left x. The
angle on the right must then be 90 – x.
Now the other angles that are still unmarked can be labeled in terms of x.
Using the rule that the angles in a triangle sum to 180°, the angle between 12
and 13 must be 90 – x, while the last angle on the right must be x,
Since each triangle has angles of 90, x, and 90 – x, the triangles are similar.
This observation is the key to the problem. Now you can make a proportion,
carefully tracking which side corresponds to which. The 7.2 corresponds to
12, since each side is across from angle x. Likewise, k corresponds to 13,
since each side is the hypotenuse. Write the equation and solve for k:
7.2/12=k/13
k=13*7.2/12
k=7.8
