Question

Tammy is mapping a portion of a fence line on her property. The fence runs along the property from point K to point L, and then turns at point L and runs directly to point M. Tammy has measured the lengths of AB and BC as well as AC and found the lengths to be 290 yards, 248 yards, and 499 yards respectively. By what angle does the fence line change direction? (Round your answer to the nearest degree if necessary. Do not include any units.)

Answer 1

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 44

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

$cos(C) = -\dfrac{103390}{143840}$

$\angle C = arccos \left( -\dfrac{103390}{143840} \right) \approx 135.95^{\circ}$

∠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 44

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