B. Xy-2y-4x=0 - Gauthmath

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Question

In △ KLM , the measure of ∠ M=90°, KM=56, ML=33 , and LK=65. What is the value of the sine of ∠ L to the nearest hundredth?SHOW LESS192

Solution

The answer is 0.51.

Step 1: Identify the sides of the triangle relative to angle L. In triangle ( KLM ), we have a right triangle with ( \angle M = 90^\circ ). The sides are as follows:

  • ( KM = 56 ) (adjacent to ( \angle L ))
  • ( ML = 33 ) (opposite to ( \angle L ))
  • ( LK = 65 ) (hypotenuse)

Step 2: Use the definition of sine. The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Therefore, we can express ( \sin L ) as follows: [ \sin L = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{ML}{LK} ]

Step 3: Substitute the known values into the sine formula. [ \sin L = \frac{33}{65} ]

Step 4: Calculate the value of ( \sin L ). Perform the division: [ \sin L = \frac{33}{65} \approx 0.5076923077 ]

Step 5: Round to the nearest hundredth. Rounding ( 0.5076923077 ) to the nearest hundredth gives ( 0.51 ).

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