Question

Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree.

Answer 1

2nd option

Explanation:

Using the sine and cosine ratios in the right triangle

sin82° =
`(opposite)/(hypotenuse)` =
`(KL)/(KM)` =
`(KL)/(√(11) )` ( multiply both sides by
`√(11)` )

`\sqrt11}` × sin82° = KL , then

KL ≈ 3.28 ( to the nearest hundredth )

cos82° =
`(adjacent)/(hypotenuse)` =
`(ML)/(KM)` =
`(ML)/(√(11) )` ( multiply both sides by
`√(11)` )

`√(11)` × cos82° = ML , then

ML ≈ 0.46 ( to the nearest hundredth )

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The sum of the 3 angles in a triangle = 180° , so

∠ K = 180° - (90 + 82)° = 180° - 172° = 8°