How to find the third side of an obtuse triangle

Asked by admin @ 23/11/2021 in Mathematics viewed by 333 People

ΔEFG is an obtuse triangle. Two of its sides measure 13 cm and 7 cm. What is the range of possible values for its third side to the nearest tenth of a centimeter?

Answered by admin @ 23/11/2021

Answer:

6 cm to 10.9 cm or 14.8 cm to 20 cm

Step-by-step explanation:

The longest of the two given sides can be the longest side, or it can be the second-longest side.

If 13 cm is the second-longest side, the triangle will be a right triangle for the longest side being ...

√(13² +7²) = √218 ≈ 14.76

That is, if the longest side is 14.8 cm up to the maximum of 13+7 = 20 cm, the triangle will be obtuse.

Similarly, if 13 cm is the longest side, then the other side in a right triangle will be ...

√(13² -7²) = √120 ≈ 10.954

For a side length shorter than this down to 13-7 = 6 cm, the triangle will also be obtuse.

The triangle will be obtuse for a long side between 14.8 and 20 cm, or for a third side between 6 and 10.9 cm.

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