In analyzing the given diagram which is a combination of two right angle triangle, the value of sin∠L is 5/13.
<h3>What is the value of sin∠L?</h3>
Given that angle ONM is a right angled triangle, we can find length of OM using the Pythagorean theorem.
c = √( a² + b² )
OM = √( 4² + 3² )
OM = √( 16 + 9 )
OM = √25
OM = 5
Next, angle OML is also a right angled triangle, we can get the hypotenuse LO.
c = √( a² + b² )
LO = √( OM² + ML² )
LO = √( 5² + 12² )
LO = √( 25 + 144 )
LO = √169
LO = 13
Now, to get sin∠L, we use the mnemonic: SOHCAHTOA
sinθ = opposite / hypotenuse
sin∠L = OM / LO
sin∠L = 5/13
Therefore, in analyzing the given diagram which is a combination of two right angle triangle, the value of sin∠L is 5/13.
Learn more about Pythagorean theorem here: brainly.com/question/343682
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