Find KL round to nearest tenth

9514 1404 393

  KL ≈ 5.3

Step-by-step explanation:

JL/JM = tan(51°)   ⇒   JL = JM×tan(51°)

KL/JL = cos(72°)   ⇒   KL = JL×cos(72°) = JM×tan(51°)×cos(72°)

KL = 14·tan(51°)·cos(72°) ≈ 5.3

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step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4