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 ) 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 ) ft

Explanation:

Step1: Find $a$ via Pythagoras

$a = \sqrt{12^2 + 5^2}$

Step2: Calculate value of $a$

$a = \sqrt{144 + 25} = \sqrt{169} = 13$

Step3: Find $b$ via Pythagoras

$b = \sqrt{a^2 + 5^2} = \sqrt{13^2 + 5^2}$

Step4: Calculate and round $b$

$b = \sqrt{169 + 25} = \sqrt{194} \approx 13.9$

Answer:

(a) $a = 13$ ft
(b) $b = 13.9$ ft