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

Question

2304 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-26T06:51:28

In both cases, triangle is obtuse

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

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. $ˆ F$ $hat F$ - One acute and another obtuse angle.

Case 1: $ˆ F$ $hat F$ acute.

$sin F = \frac{f sin D}{d} = \frac{24 \cdot sin 15}{18} = 0.3451$ $sin F = (f sin D) / d = (24 * sin 15) / 18 = 0.3451$

$ˆ F = {sin}^{- 1} 0.3451 = {20.19}^{\circ}$ $hat F = sin ^-1 0.3451 = 20.19^@$

$ˆ E = 180 - 15 - 20.19 = {144.81}^{\circ}$ $hat E = 180 - 15 - 20.19 = 144.81^@$

Case 2: $ˆ F$ $hat F$ obtuse.

$sin F = \frac{f sin D}{d} = \frac{24 \cdot sin 15}{18} = 0.3451$ $sin F = (f sin D) / d = (24 * sin 15) / 18 = 0.3451$

$ˆ F = {sin}^{- 1} 0.3451 = 180 - 20.19 = {159.81}^{\circ}$ $hat F = sin ^-1 0.3451 = 180 - 20.19 = 159.81^@$

$ˆ E = 180 - 15 - 159.81 = {5.19}^{\circ}$ $hat E = 180 - 15 - 159.81 = 5.19^@$

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