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የያንዳንዱን ርዝመት የእያንዳንዱን የጎን ርዝመት መርምረህ አንዳንዱን እያንዳንዳቸውን አስገባ። ሀ. 7ሴ.ሜ. 4ሴ.ሜ. እና 6ሴ.ሜ. ለ. 8ሴ.ሜ. 8ሴ.ሜ. እና 8ሴ.ሜ. ሐ. 6ሴ.ሜ. 6ሴ.ሜ. እና 10ሴ.ሜ. መ. 2ሴ.ሜ. 9ሴ.ሜ. እና 6ሴ.ሜ. የያንዳንዱን የጎን ርዝመት በሰንጠረዡ መሠረት የጐን ርዝመት 3ሴ.ሜ.: ሀ. 4=6ሴ.ሜ. 4=8ሴ.ሜ. እና 9=9ሴ.ሜ. ለ. <4 =50° : < =50° እና 2.6 = 6ሴ.ሜ.

Mathematics

ScanSolve AI Answer

: Finding ∠A\angle A in △ABC\triangle ABC

Sum of angles in a triangle:

∠A=180∘−∠B−∠C\angle A = 180^\circ - \angle B - \angle C ∠A=180∘−71∘−67∘=42∘\angle A = 180^\circ - 71^\circ - 67^\circ = 42^\circ

∠A=42∘\angle A = 42^\circ

: Finding side bb in △ABC\triangle ABC

Law of sines:

asin⁡∠A=bsin⁡∠B\frac{a}{\sin \angle A} = \frac{b}{\sin \angle B} b=a⋅sin⁡∠Bsin⁡∠A=5 cm⋅sin⁡71∘sin⁡42∘b = a \cdot \frac{\sin \angle B}{\sin \angle A} = 5~\mathrm{cm} \cdot \frac{\sin 71^\circ}{\sin 42^\circ}

sin⁡42∘≈0.6694\sin 42^\circ \approx 0.6694, sin⁡71∘≈0.9455\sin 71^\circ \approx 0.9455

sin⁡71∘sin⁡42∘≈0.94550.6694≈1.412\frac{\sin 71^\circ}{\sin 42^\circ} \approx \frac{0.9455}{0.6694} \approx 1.412 b≈5 cm×1.412=7.06 cmb \approx 5~\mathrm{cm} \times 1.412 = 7.06~\mathrm{cm}

b=7.06 cmb = 7.06~\mathrm{cm}

: Finding side cc in △ABC\triangle ABC

Law of sines:

asin⁡∠A=csin⁡∠C\frac{a}{\sin \angle A} = \frac{c}{\sin \angle C} c=a⋅sin⁡∠Csin⁡∠A=5 cm⋅sin⁡67∘sin⁡42∘c = a \cdot \frac{\sin \angle C}{\sin \angle A} = 5~\mathrm{cm} \cdot \frac{\sin 67^\circ}{\sin 42^\circ}

sin⁡42∘≈0.6694\sin 42^\circ \approx 0.6694, sin⁡67∘≈0.9205\sin 67^\circ \approx 0.9205

sin⁡67∘sin⁡42∘≈0.92050.6694≈1.375\frac{\sin 67^\circ}{\sin 42^\circ} \approx \frac{0.9205}{0.6694} \approx 1.375 c≈5 cm×1.375=6.88 cmc \approx 5~\mathrm{cm} \times 1.375 = 6.88~\mathrm{cm}

c=6.88 cmc = 6.88~\mathrm{cm}

: Finding ∠F\angle F in △DEF\triangle DEF

Sum of angles in a triangle:

∠F=180∘−∠D−∠E\angle F = 180^\circ - \angle D - \angle E ∠F=180∘−52∘−67∘=61∘\angle F = 180^\circ - 52^\circ - 67^\circ = 61^\circ

∠F=61∘\angle F = 61^\circ

: Finding side ee in △DEF\triangle DEF

Law of sines:

dsin⁡∠D=esin⁡∠E\frac{d}{\sin \angle D} = \frac{e}{\sin \angle E} e=d⋅sin⁡∠Esin⁡∠D=10 cm⋅sin⁡67∘sin⁡52∘e = d \cdot \frac{\sin \angle E}{\sin \angle D} = 10~\mathrm{cm} \cdot \frac{\sin 67^\circ}{\sin 52^\circ}

sin⁡52∘≈0.7880\sin 52^\circ \approx 0.7880, sin⁡67∘≈0.9205\sin 67^\circ \approx 0.9205

sin⁡67∘sin⁡52∘≈0.92050.7880≈1.168\frac{\sin 67^\circ}{\sin 52^\circ} \approx \frac{0.9205}{0.7880} \approx 1.168 e≈10 cm×1.168=11.68 cme \approx 10~\mathrm{cm} \times 1.168 = 11.68~\mathrm{cm}

e=11.68 cme = 11.68~\mathrm{cm}

: Finding side ff in △DEF\triangle DEF

Law of sines:

dsin⁡∠D=fsin⁡∠F\frac{d}{\sin \angle D} = \frac{f}{\sin \angle F} f=d⋅sin⁡∠Fsin⁡∠D=10 cm⋅sin⁡61∘sin⁡52∘f = d \cdot \frac{\sin \angle F}{\sin \angle D} = 10~\mathrm{cm} \cdot \frac{\sin 61^\circ}{\sin 52^\circ}

sin⁡52∘≈0.7880\sin 52^\circ \approx 0.7880, sin⁡61∘≈0.8746\sin 61^\circ \approx 0.8746

sin⁡61∘sin⁡52∘≈0.87460.7880≈1.110\frac{\sin 61^\circ}{\sin 52^\circ} \approx \frac{0.8746}{0.7880} \approx 1.110 f≈10 cm×1.110=11.10 cmf \approx 10~\mathrm{cm} \times 1.110 = 11.10~\mathrm{cm}

f=11.10 cmf = 11.10~\mathrm{cm}

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