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In △ JKL, k=87cm, l=76cm and ∠ J=82°. Find the length of j, to the nearest centimeter.

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Final answer:

To find the length of side j in triangle JKL, apply the Law of Cosines with the given side lengths and angle J. Compute j² = 87² + 76² - 2*87*76*cos(82°), and then take the square root of j². Round the result to the nearest centimetre.

Step-by-step explanation:

To find the length of side j in △ JKL, you can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles. Here, you have sides k=87cm, l=76cm, and ∠ J=82°, and you need to find j. The Law of Cosines is written as:

j² = k² + l² - 2kl · cos(∠ J)

Substituting the given values:

j² = 87² + 76² - 2 · 87 · 76 · cos(82°)

After calculating, take the square root of to find the length of side j, and round to the nearest centimetre.

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