To solve for the length of m, we can use the Law of Sines.
The Law of Sines states that for any triangle with sides a, b, and c opposite angles A, B, and C, respectively, the following relation holds:
sin(A)/a = sin(B)/b = sin(C)/c
In this case, we have k = 1 inch, l = 5.7 inches, and ∠M = 46°. We are trying to find the length of m.
We can set up the equation: sin(M)/m = sin(K)/k
Since k = 1 inch and ∠M = 46°, we can substitute these values into the equation:
sin(46°)/m = sin(K)/1
To solve for sin(K), we need to find ∠K. We know that the sum of the angles in a triangle is 180°:
∠K + ∠L + ∠M = 180°
Since ∠M = 46° and ∠L = 180° - ∠K - ∠M (opposite angles of a triangle), we can substitute these values into the equation:
∠K + (180° - ∠K - 46°) + 46° = 180°
Simplifying the equation, we get:
∠K + 134° = 180°
∠K = 180° - 134°
∠K = 46°
Now, we can substitute the values into the equation we initially set up:
sin(46°)/m = sin(46°)/1
Since sin(46°) is the same on both sides of the equation, we can simplify the equation to:
1/m = 1/1
Solving for m, we find:
m = 1 inch
Therefore, the length of m is 1 inch.
In ΔKLM, k = 1 inches, l = 5.7 inches and ∠M=46°. Find the length of m, to the nearest 10th of an inch.
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