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Two angles of a spherical triangle measure 36° and 62°. What is the range for the...

Two angles of a spherical triangle measure 36° and 62°. What is the range for the measure of the third angle? Answer in this form: __<x<___

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Answer #1

We know that sum of all angles in a spherical triangle lies between to 3 or 180 to 540 degrees.

let A, B, and C be the three angles of a spherical triangle. so according to this fact

as given in the question.

So, putting them in the above relation we get

by subtracting 36+62 (=98) from all sides we get

or

so,the range of the third angle is 82 to 442 degrees respectively.

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