The figure shows a 129-meter long
bridge on supports 𝑀𝐶 and 𝑀𝐷 attached at the midpoint 𝑀. If 𝐴𝐶 is equal to 51.6 meters,
find the length of 𝑀𝐶 to the nearest hundredth.
We are told in the question that
the length of the bridge 𝐴𝐵 is 129 meters. As 𝑀 is the midpoint of 𝐴𝐵, we
can calculate the distance 𝐴𝑀 by dividing 129 by two. This is equal to 64.5 meters. We are also told that the length
𝐴𝐶 is 51.6 meters. 𝐴𝑀𝐶 is a right triangle where we
know two lengths and need to calculate the length 𝑀𝐶.
We can do this using the
Pythagorean theorem. This states that 𝑎 squared plus 𝑏
squared is equal to 𝑐 squared. 𝑐 is the longest side of the right
triangle, known as the hypotenuse. In this case, this is the length
𝑀𝐶. Substituting in our values gives us
64.5 squared plus 51.6 squared is equal to 𝑥 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 𝑥.
𝑥 is equal to
[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
𝑀𝐶, to the nearest hundredth, is 82.60 meters.