Collins Park has a pine tree, an oak tree, and a maple tree on the three corners of the triangular park. The angle formed at the oak tree measures 70*, The distance between the oak tree and the maple tree is 90 leet, and the angle formed at the pine tree measures 90'. Bertha is trying to determine the other measures created by their positions. Give each measurement rounded to the nearest thousandth of a foot.

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sqdancefan sqdancefan · Answer 1 · 2024-01-21T02:36:58+01:00

Answer:

Step-by-step explanation:

You want the unknown measures in ∆POM with O=70°, P=90°, OM=90 ft.

The 90° angle at the pine tree tells you this is a right triangle. The unknown angle at the maple tree will be the complement of 70*, or 20°

The hypotenuse of the triangle is given, so the other sides can be found using the sine and cosine functions.

o = PM = OM·sin(70°) = (90 ft)sin(70°) ≈ 84.572 ft — pine to maple

m = PO = OM·cos(70°) = (90 ft)cos(70°) ≈ 30.782 ft — pine to oak

M = 180° -90° -70° = 20° — angle at maple