Answer:
8
Step-by-step explanation:
Hello,
This is related to ratios and proportions. We have a 12 foot tree that casts a 6 foot shadow, so now we are trying to figure out how tall is a tree that casts a 4 foot shadow.
We can set an easier method to get this.
12 = 6 (this means the 12 foot tree casts a 6 foot shadow)
x = 4 (this means how tall is the tree to cast a 4 foot shadow, the unknown height of the tree is denoted as x)
Then, we can cross multiply.
48 = 6x
Solve for x, which is the unknown height we are trying to figure out.
x = 8
The square root of 343 is 18.520 or 18.52 or also 18
Answer: x = 50
Concept:
Here, we need to know the idea of alternative interior angles and the angle sum theorem.
<u>Alternative interior angles</u> are angles that are formed inside the two parallel lines, and the values are equal.
The <u>angle sum theorem</u> implies that the sum of interior angles of a triangle is 180°
If you are still confused, please refer to the attachment below or let me know.
Step-by-step explanation:
<u>Given information:</u>
AC ║ DE
∠ABC = 85°
∠A = 135°
<u>Find the value of ∠BAC</u>
∠A + ∠BAC = 180° (Supplementary angle)
(135°) + ∠BAC = 180°
∠BAC = 45°
<u>Find the value of ∠BCA</u>
∠ABC + ∠BAC + ∠BCA = 180° (Angle sum theorem)
(85°) + (45°) + ∠BCA = 180°
∠BCA = 50°
<u>Find the value of x (∠EBC)</u>
∠EBC ≅ ∠BCA (Alternative interior angles)
Since, ∠BCA = 50°
Therefore, ∠EBC = 50°

Hope this helps!! :)
Please let me know if you have any questions