Question

a tent has the shape of an isosceles triangular prism. the campers add a pole of length b (in feet) for extra support that goes from the top front corner to one of the back bottom corners, as shown in the figure. (the figure is not drawn to scale.)
(a) find a.
( a=square mathrm{ft} )
(b) use your answer to part (a) to find ( b ), the length of the pole. round your answer to the nearest tenth of a foot.
( b=square mathrm{ft} )

Explanation:

Step1: Find \(a\) using the Pythagorean theorem

The Pythagorean theorem for a right - triangle is \(c^{2}=x^{2}+y^{2}\), where \(c\) is the hypotenuse.
For the right - triangle with legs \(8\) ft and \(6\) ft, \(a=\sqrt{8^{2}+6^{2}}\).

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Step2: Find \(b\) using the Pythagorean theorem

Now consider the right - triangle with legs \(a = 10\) ft and \(16\) ft.
By the Pythagorean theorem \(b=\sqrt{a^{2}+16^{2}}\).
Substitute \(a = 10\) into the formula:

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Answer:

(a) \(a = 10\) ft
(b) \(b\approx18.9\) ft