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Triangle $EFG$ on one side $FG$ measures $20\,\text{m}$ and angle $\text{DEF}$ is $60$ degrees. $EG$ bisects angle $\text{DEF}$

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Find missing angles in triangles using ratios

Full solution

Q. Triangle

EFG

on one side

FG

measures

20\,\text{m}

and angle

\text{DEF}

is

60

degrees.

EG

bisects angle

\text{DEF}

Calculate EG Length: Calculate the length of side $EG$ using the fact that angle $EGF$ is $30$ degrees because $EG$ bisects angle $DEF$ which is $60$ degrees.
Trigonometry Calculation: Use the sine rule or trigonometry to find the length of side $EG$ . Since we don't have enough information to apply the sine rule, we'll use trigonometry.
Sine Function Application: In right triangle $EGF$ , side $EG$ is the hypotenuse and side $FG$ is opposite to the $30$ -degree angle. Use the sine function: $\sin(30) = \frac{FG}{EG}$ .
Solve for EG: $\sin(30)$ is $0.5$ . So, $0.5 = \frac{20 m}{EG}$ . Solve for EG by multiplying both sides by EG and then dividing both sides by $0.5$ .
Final Calculation: $EG \times 0.5 = 20 \, \text{m}$ . Therefore, $EG = \frac{20 \, \text{m}}{0.5}$ .
Result: $EG = 40\,\text{m}$ . So, the length of side $EG$ is $40\,\text{meters}$ .

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