How do you determine the number of possible triangles and find the measure of the three angles given $DE=24, EF=18, mangleD=15$ ?

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Answer 1 · 2018-02-26T06:51:28

In both cases, triangle is obtuse

Case (1) : $hat D = 15, hat E = 144.81, hat F = 20.19$

Case (2) : #hat D = 15, hat E = 5.19 enter image source here , hat F = 159.81#

Two solutions possible with the given SSA measurements. $hat F$ - One acute and another obtuse angle.

Case 1: $hat F$ acute.

$sin F = (f sin D) / d = (24 * sin 15) / 18 = 0.3451$

$hat F = sin ^-1 0.3451 = 20.19^@$

$hat E = 180 - 15 - 20.19 = 144.81^@$

Case 2: $hat F$ obtuse.

$sin F = (f sin D) / d = (24 * sin 15) / 18 = 0.3451$

$hat F = sin ^-1 0.3451 = 180 - 20.19 = 159.81^@$

$hat E = 180 - 15 - 159.81 = 5.19^@$

How do you determine the number of possible triangles and find the measure of the three angles given DE=24, EF=18, mangleD=15DE=24, EF=18, mangleD=15?