Based on the calculations, the length of AB is equal to 18 units.
How to determine the magnitude of each length?
In order to determine the length of AB, we would apply Pythagorean theorem since the triangle is right-angled.
Mathematically, Pythagorean's theorem is given by this formula:
c² = a² + b²
15² = 12² + b²
225 = 144 + b²
b² = 225 - 144
b = √81
b = 9 units.
Length AB = 2b
Length AB = 2 × 9
Length AB = 18 units.
Part 2.
For m<DBC, we have:
By critically observing the triangle, we can deduce that it is a complimentary angle (90°)
90 = m<DBC + m<BAC
m<DBC = 90 - 60
m<DBC = 30°.
Part 3.
For the length DE, we have:
AE × BE = CE × DE
35 × (35 - 30) = 25 × DE
35 × 5 = 25 × DE
175 = 25DE
DE = 175/25
DE = 7 units.
Part 4.
For the length DE, we have:
AC × CB = CD × DE
8 × (15 - 8) = 4 × DE
8 × 7 = 4 × DE
56 = 4DE
DE = 56/4
DE = 14 units.
Part 5.
For m<ABC, we have:
First of all, we would determine the magnitude of m<AXC:
m<AXC = 360 - 106
m<AXC = 254°.
Now, we can determine the magnitude of m<ABC:
m<ABC = (254 - 106)/2
m<ABC = 148/2
m<ABC = 74°.
Read more on Pythagorean theorem here: https://brainly.com/question/16176867
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