Answer:
1.) 9.9
2.) 15.6
Step-by-step explanation:
1.) Consider triangle AEH
AEH is a right angle triangle as ∠AEH = 90°
AH is the hypotenuse of the triangle.
Applying Pythagorean theorem
[tex]AE^{2} + EH^{2} = AH^{2}[/tex]
substituting values as given in the question:
[tex]7^{2} +EH^{2}=(7\sqrt{3} )^{2}\\EH^{2}=(7\sqrt{3} )^{2}-7^{2} \\EH^{2}=98\\EH=\sqrt{98}\\EH=7\sqrt{2}[/tex]
∴ EH≈9.9
2.) Consider triangle CDF
CDF is a right angle triangle as ∠CDF = 90°
CF is the hypotenuse of the triangle.
Applying Pythagorean theorem
[tex]CD^{2} + DF^{2} = CF^{2}[/tex]
substituting values as given in the question:
[tex]11^{2} +DF^{2}=(11\sqrt{3} )^{2}\\DF^{2}=(11\sqrt{3} )^{2}-11^{2} \\DF^{2}=242\\DF=\sqrt{242}\\DF=11\sqrt{2}[/tex]
∴ DF≈15.6
