Answer:
m∠EBC = 65.25°
AC=20 in.
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 equal 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
Dividing both sides by 2 we get;
∠BAE=24.75°
Now in triangle ΔBEC we have:
∠BEC=90° , ∠BCE=24.75°
SO,
∠BEC+∠BCE+∠EBC=180°.
Hence, [tex]90+24.75+ \angle EBC=180[/tex]
∠EBC=[tex]180-(90+24.75)[/tex]
∠EBC=65.25°
Now we are given AE = 10 in
Also ∠BEA= 90°.
And ∠BAE=24.75°; hence using trigonometric identity to find the measure of side BE.
[tex]tan24.75=\frac{BE}{AE} = \frac{BE}{10}\\\\BE= 10 \ tan24.75 \ \ \ \ \ equation \ 2[/tex]
similarly in right angled triangle ΔBEC we have:
[tex]tan24.75=\frac{BE}{EC}\\\\EC=\frac{BE}{tan24.75} \ \ \ \ \ \ \ \ \ equation \ 3[/tex]
Hence, using equation (2) in equation (3) we get:
[tex]EC = \frac{10 \ tan24.75}{tan24.75} =10in[/tex]
Hence AC=AE+EC=10+10=20 in.
Hence side AC=20 in.
Answer: uhhhh, what is the minute, just have this question
Step-by-step explanation:
