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In ΔHIJ\Delta HIJ, i=970i = 970 inches, j=660j = 660 inches and ∠H=82∘\angle H=82^\circ. Find the length of hh, to the nearest inch.

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Full solution

Q. In ΔHIJ\Delta HIJ, i=970i = 970 inches, j=660j = 660 inches and ∠H=82∘\angle H=82^\circ. Find the length of hh, to the nearest inch.
  1. Prompt: question_prompt: How long is side hh in ΔHIJ\Delta HIJ to the nearest inch?
  2. Law of Cosines Formula: We can use the Law of Cosines to find hh since we have two sides and the included angle. The formula is h2=i2+j2−2ijcos⁡(H)h^2 = i^2 + j^2 - 2ij\cos(H).
  3. Plug in Values: Plug in the values: h2=9702+6602−2×970×660×cos⁡(82°)h^2 = 970^2 + 660^2 - 2 \times 970 \times 660 \times \cos(82°).
  4. Calculate Squares: Calculate the squares: h2=940900+435600−2×970×660×cos⁡(82°)h^2 = 940900 + 435600 - 2 \times 970 \times 660 \times \cos(82°).

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