Answer:
Step-by-step explanation:
We are given AB
≅
BC that means that side AB and side BC are equal also we know that angle opposite to equalt
sides are equal.
Hence, ∠BAE=∠BCE-------(1)
Also ∠AEB=∠CEB.
Now we are given that: ∠ABC = 130°30’ i.e. in degrees it could be given as:
60'=1°
30'=(1/2)°=0.5°
Hence ∠ABC = 130°30’=130+0.5=130.5°
Also we know that sum of all the angles in a triangle is equal to 180°.
Hence,
∠BAE+∠BCE+∠ABC=180°.
2∠BAE+130.5=180 (using equation (1))
2∠BAE=49.5
∠BAE=24.75° (DIVIDE BOTH SIDE BY 2)
Now in triangle ΔBEC we have:
∠BEC=90° , ∠BCE=24.75°
SO,
∠BEC+∠BCE+∠EBC=180°.
Hence, 90+24.75+∠EBC=180
∠EBC=180-(90+24.75)
∠EBC=65.25°
Now we are given AE = 10 in
Also ∠BEA= 90°.
And ∠BAE=24.75°; hence using trignometric identity to find the measure of side BE.
[tex]\tan 24.75=\dfrac{BE}{AE}=\dfrac{BE}{10}\\\\BE=10\tan 24.75-------(2)[/tex]
similarly in right angled triangle ΔBEC we have:
[tex]\tan 24.75=\dfrac{BE}{EC}\\\\\tan 24.75=\dfrac{BE}{EC}\\\\EC=\dfrac{BE}{\tan 24.75}------(3)[/tex]
Hence, using equation (2) in equation (3) we get:
[tex]EC=10 \text{in.}[/tex]
Hence AC=AE+EC=10+10=20 in.
Hence side AC=20 in.
