If Q, O, equals, QO=56, O, P, equals, OP=83, and R, S, equals, RS=29, find the length of start overline, T, R, end overline
TR
. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.
To find the length of TR, we first need to calculate the distance between T and R using the Pythagorean theorem.
From the given information, we have:
1. QT = QO + OP = 56 + 83 = 139
2. TS = TR + RS = TR + 29
Now, applying the Pythagorean theorem to triangle QTS:
(QT)^2 = (TR + RS)^2 + (QO)^2
(139)^2 = (TR + 29)^2 + (56)^2
19321 = (TR + 29)^2 + 3136
19321 - 3136 = (TR + 29)^2
16185 = (TR + 29)^2
Now, taking the square root of both sides:
127.3 ≈ TR + 29
Subtracting 29 from both sides, we get:
TR ≈ 98.3
Therefore, the length of TR is approximately 98.3.