Question

Use the laws of sine and cosine to find the missing Dimension part 3

Find the f to the nearest whole number​

Answer 1

• 103

Explanation:

Find ∠E

• sin E / 71 = sin 36° / 62
• sin E = 71 (sin 36°) / 62
• sin E = 0.673
• m∠E = arcsin (0.673)
• m∠E = 42° (rounded)

Find m∠F

• m∠F = 180° - (36° + 42°) = 102

Find f

• sin 102° / f = sin 36° / 62
• f = (62 sin 102°) / (sin 36°)
• f = 103 (rounded)

Answer 2

9514 1404 393

Answer:

12 or 103

Explanation:

The given angle is opposite the shorter side, so there will be two solutions.

In order to find f, we need to know angle F. We can find that by first finding angle E.

E = arcsin(e/d·sin(D)) = arcsin(71/62·sin(36°)) = 42.307° or 137.693°

F = 180° -D -E = 180° -36° -{42.307°, 137.693°} = {101.693°, 6.307°}

Then the measure of f is ...

f = sin(F)/sin(D)×d = 62/sin(36°)×sin({101.693°, 6.307°})

f = {103.29, 11.59}

Side f is either 12 or 103.