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.

Question

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.

ScanSolve AI Tutor · Accepted Answer

**Exercise 1a: Finding $\angle A$ in $	riangle ABC$**

Sum of angles in a triangle:  
$$
\angle A = 180^\circ - \angle B - \angle C
$$  
$$
\angle A = 180^\circ - 71^\circ - 67^\circ = 42^\circ
$$  
**$\angle A = 42^\circ$**

**Exercise 1b: Finding side $b$ in $	riangle ABC$**

Law of sines:  
$$
\frac{a}{\sin \angle A} = \frac{b}{\sin \angle B}
$$  
$$
b = a \cdot \frac{\sin \angle B}{\sin \angle A} = 5~\mathrm{cm} \cdot \frac{\sin 71^\circ}{\sin 42^\circ}
$$  
$\sin 42^\circ \approx 0.6694$, $\sin 71^\circ \approx 0.9455$  
$$
\frac{\sin 71^\circ}{\sin 42^\circ} \approx \frac{0.9455}{0.6694} \approx 1.412
$$  
$$
b \approx 5~\mathrm{cm} 	imes 1.412 = 7.06~\mathrm{cm}
$$  
**$b = 7.06~\mathrm{cm}$**

**Exercise 1c: Finding side $c$ in $	riangle ABC$**

Law of sines:  
$$
\frac{a}{\sin \angle A} = \frac{c}{\sin \angle C}
$$  
$$
c = a \cdot \frac{\sin \angle C}{\sin \angle A} = 5~\mathrm{cm} \cdot \frac{\sin 67^\circ}{\sin 42^\circ}
$$  
$\sin 42^\circ \approx 0.6694$, $\sin 67^\circ \approx 0.9205$  
$$
\frac{\sin 67^\circ}{\sin 42^\circ} \approx \frac{0.9205}{0.6694} \approx 1.375
$$  
$$
c \approx 5~\mathrm{cm} 	imes 1.375 = 6.88~\mathrm{cm}
$$  
**$c = 6.88~\mathrm{cm}$**

**Exercise 2a: Finding $\angle F$ in $	riangle DEF$**

Sum of angles in a triangle:  
$$
\angle F = 180^\circ - \angle D - \angle E
$$  
$$
\angle F = 180^\circ - 52^\circ - 67^\circ = 61^\circ
$$  
**$\angle F = 61^\circ$**

**Exercise 2b: Finding side $e$ in $	riangle DEF$**

Law of sines:  
$$
\frac{d}{\sin \angle D} = \frac{e}{\sin \angle E}
$$  
$$
e = d \cdot \frac{\sin \angle E}{\sin \angle D} = 10~\mathrm{cm} \cdot \frac{\sin 67^\circ}{\sin 52^\circ}
$$  
$\sin 52^\circ \approx 0.7880$, $\sin 67^\circ \approx 0.9205$  
$$
\frac{\sin 67^\circ}{\sin 52^\circ} \approx \frac{0.9205}{0.7880} \approx 1.168
$$  
$$
e \approx 10~\mathrm{cm} 	imes 1.168 = 11.68~\mathrm{cm}
$$  
**$e = 11.68~\mathrm{cm}$**

**Exercise 2c: Finding side $f$ in $	riangle DEF$**

Law of sines:  
$$
\frac{d}{\sin \angle D} = \frac{f}{\sin \angle F}
$$  
$$
f = d \cdot \frac{\sin \angle F}{\sin \angle D} = 10~\mathrm{cm} \cdot \frac{\sin 61^\circ}{\sin 52^\circ}
$$  
$\sin 52^\circ \approx 0.7880$, $\sin 61^\circ \approx 0.8746$  
$$
\frac{\sin 61^\circ}{\sin 52^\circ} \approx \frac{0.8746}{0.7880} \approx 1.110
$$  
$$
f \approx 10~\mathrm{cm} 	imes 1.110 = 11.10~\mathrm{cm}
$$  
**$f = 11.10~\mathrm{cm}$**

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