Answer:
Length of the kite’s shorter diagonal = 39.03 inches
Step-by-step explanation:
Refer the given figure, we need to find DB,
Consider ΔABC,
Using cosine rule
[tex]cos B=\frac{a^2+c^2-b^2}{2ac}[/tex]
a = c = 41 inches
b = 80 inches
We need to find ∠B
Substituting
[tex]cos B=\frac{41^2+41^2-80^2}{2\times 41\times 41}=-0.903\\\\B=154.56^0[/tex]
We can see that BD divides ∠B equally,
So, [tex]\angle ABD=\frac{\angle B}{2}=\frac{154.56}{2}=77.28^0[/tex]
Now consider ΔABD,
Using sine rule
[tex]\frac{AB}{sinD}=\frac{AD}{sinB}=\frac{DB}{sinA}[/tex]
AB = 41 inches, AD = 50 inches, ∠B = 77.28°
Substituting
[tex]\frac{41}{sinD}=\frac{50}{sin77.28}=\frac{DB}{sinA}\\\\sinD=0.7999\\\\D=53.12^0\\\\A=180-53.12-77.28=49.6^0\\\\\frac{50}{sin77.28}=\frac{DB}{sin49.6}\\\\DB=39.03inch[/tex]
Length of the kite’s shorter diagonal = 39.03 inches
Answer:
The answer is 39 on edge. :)
Step-by-step explanation:
