Question

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

Answer 1

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 , hat F = 159.81`

Explanation:

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^@`