How do you determine the number of possible triangles and find the measure of the three angles given $a = 8, b = 10, m ∠ A = 45$ $a=8, b=10, mangleA=45$ ?

Question

2548 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-26T06:24:27

Solution (1) $ˆ . = 45^{\circ}, ˆ B = {62.12}^{\circ}, ˆ C = {72.88}^{\circ}$ $hat. = 45^@, hat B = 62.12^@, hat C = 72.88^@$

Solution (2) $ˆ . = 45^{\circ}, ˆ B = {117.88}^{\circ}, ˆ C = {17.12}^{\circ}$ $hat. = 45^@, hat B = 117.88^@, hat C = 17.12^@$

$ˆ A = 45, a = 8, b = 10$ $hat A = 45, a = 8, b = 10$

Applying law of sines,

$sin B = \frac{sin A \cdot b}{a} = \frac{sin 45 \cdot 10}{8} \approx 0.8839$ $sin B = (sin A * b) / a = (sin 45 * 10) / 8 ~~ 0.8839$

$ˆ B = {sin}^{- 1} 0.8839 \approx 62.12$ $hat B = sin ^-1 0.8839 ~~ 62.12$

$ˆ C = 180 - 45 - 62.12 = {72.88}^{\circ}$ $hat C = 180 - 45 - 62.12 = 72.88^@$

enter image source here

Since $ˆ A + ˆ B = 45 + 62.12 = 107.12$ $hat A + hatB = 45 + 62.12 = 107.12$ is less than $180^{\circ}$ $180^@$ , we will have one more solution.

Supplementary angle of $ˆ B = 180 - 62.12 = {117.88}^{\circ}$ $hat B = 180 - 62.12 = 117.88^@$

$ˆ C = 180 - 117.88 - 45 = {17.12}^{\circ}$ $hat C = 180 - 117.88 - 45 = 17.12^@$

enter image source here

How do you determine the number of possible triangles and find the measure of the three angles given a=8,b=10,m∠A=45a=8, b=10, mangleA=45?