Question

1. refer to the map of the woodlands camp at the right. round your answers to the nearest tenth.

a. how far is it from sycamore cabin to oak cabin?
b. a camper in hickory cabin wants to visit a friend in elm cabin. how much farther is it if she walks to the mess hall first?

1. justify conclusions rodrigo is buying a ( 5 \frac { 1 } { 2 } ) - foot - long fishing rod for his father for his birthday. he wants to put it in a box so that his dad will not be able to guess what is in the box. the box he wants to use is 4 feet long and 4 feet wide. will the pole fit in the box? justify your reasoning.

Explanation:

Step1: Solve part a

We can use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) for the right - triangle formed by the path from Sycamore to Oak. Here \(a = 30\) yd and \(b=40\) yd.

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Step2: Solve part b

First, find the direct distance from Hickory to Elm. Using the Pythagorean theorem with \(a = 60\) yd and \(b = 40\) yd (from the map's right - triangle structure).

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The distance via the Mess Hall is \(30 + 40=70\) yd.
The difference \(d=72.1-70 = 2.1\) yd

Step3: Solve problem 6

For the box (a square with side \(s = 4\) ft), the length of the diagonal \(d\) (using the Pythagorean theorem \(a=b = 4\) ft) is:

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Since \(5.7>5.5\) (because \(5\frac{1}{2}=5.5\)), the fishing rod will fit.

Answer:

a. \(50\) yd
b. \(2.1\) yd

1. Yes, the fishing rod will fit. The diagonal of the box (\(\approx5.7\) ft) is longer than the length of the fishing rod (\(5.5\) ft).