Two search teams spot a stranded climber between them on a mountain. The first team is $\displaystyle {0.6}$ miles from the second team, and both teams are at an altitude of $\displaystyle {0.2}$ miles.  The angle of elevation from the first team to the stranded climber is $\displaystyle {14}$ ^o . The angle of elevation from the second team to the climber is $\displaystyle {23}$ ^o  . What is the altitude of the climber? Round to the nearest hundredth of a mile.

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