Sophie has a doll collection with 36 dolls. She decides to sell s dolls to a museum and has r dolls remaining.
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Given the lengths of the three sides of the triangular fence, the angle by
which the fence line changes direction can be found by cosine rule.
The angle by which the fence line change direction is approximately <u>44</u>
The given parameters are;
AB = 290 yards = LK
BC = 248 yards = ML
AC = 499 yards = MK
Let AB = a, BC = b, and AC = c, by cosine rule, we have;
c² = b² + a² - 2·b·a·cos(C)
Therefore;
499² = 248² + 290² - 2×248×290×cos(C)
2×248×290×cos(C) = 248² + 290² - 499² = -103397
143840×cos(C) = -103397
∠C = ∠ABC = ∠MLK ≈ 135.95°
The angle by which the fence turns is a supplementary angle to angle
∠MLK, which is therefore;
?° + ∠MLK = 180°
?° = 180° - ∠MLK
∴ ?° ≈ 180° - 135.95° ≈ 44°
The angle by which the fence change direction is approximately <u>44</u>
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