The Frostburg-Truth bus travels from Frostburg Mall through the city’s center to Sojourner Truth Park. The mall is 5 miles west and 4 miles south of the city’s center. Truth Park is 5 miles east and 2 miles north of the city’s center. How far is it from Truth Park to the mall to the nearest tenth of a mile?
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Thus, Truth park is 11.8 miles from the mall.
Step-by-step explanation:
In the given figure, in triangle OWS, we apply Pythagoras Theorem.
OS² = OW² + WS²
= 5² + 4²
= 25 + 16
OS = √41
In triangle OEN, again we apply the Pythagoras Theorem.
Therefore, ON² = NE² + OE²
= 5² + 2²
= 25 + 4
ON = √29
According to the figure, the distance between Truth park and the mall = SN
SN = OS + ON
=
= 6.4031 + 5.3851
= 11.7882 ≈ 11.8 miles
Thus, Truth park is 11.8 miles from the mall.
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