Question Video: Applying Pythagoras’s Theorem to Solve Complex Problems in Real-Life Contexts | Nagwa Question Video: Applying Pythagoras’s Theorem to Solve Complex Problems in Real-Life Contexts | Nagwa

# Question Video: Applying Pythagorasβs Theorem to Solve Complex Problems in Real-Life Contexts Mathematics

The figure shows a 129 m long bridge on supports ππΆ, ππ· attached at the midpoint π. If π΄πΆ = 51.6 m, find the length of ππΆ to the nearest hundredth.

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### Video Transcript

The figure shows a 129-meter long bridge on supports ππΆ and ππ· attached at the midpoint π. If π΄πΆ is equal to 51.6 meters, find the length of ππΆ to the nearest hundredth.

We are told in the question that the length of the bridge π΄π΅ is 129 meters. As π is the midpoint of π΄π΅, we can calculate the distance π΄π by dividing 129 by two. This is equal to 64.5 meters. We are also told that the length π΄πΆ is 51.6 meters. π΄ππΆ is a right triangle where we know two lengths and need to calculate the length ππΆ.

We can do this using the Pythagorean theorem. This states that π squared plus π squared is equal to π squared. π is the longest side of the right triangle, known as the hypotenuse. In this case, this is the length ππΆ. Substituting in our values gives us 64.5 squared plus 51.6 squared is equal to π₯ squared. Typing the left-hand side into our calculator gives us 6822.81. We can then square root both sides of this equation to calculate the value of π₯. π₯ is equal to 62.600302 [82.600302] and on so.

We are asked to round to the nearest hundredth, which is the same as rounding to two decimal places. As this rounds down, the length of ππΆ, to the nearest hundredth, is 82.60 meters.

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