In the figure, angle ABC and angle ADB are each right angles. Additionally, AC = 17.8 units and AD = 5 units. What is the length of segment DB?
Answers
Answer:
DB = 8
Step-by-step explanation:
Δ ADB and Δ BDC are similar so ratios of corresponding sides are equal, that is
[tex]\frac{DB}{DC}[/tex] = [tex]\frac{AD}{BD}[/tex] , substitute values
[tex]\frac{DB}{17.8-5}[/tex] = [tex]\frac{5}{BD}[/tex]
[tex]\frac{DB}{12.8}[/tex] = [tex]\frac{5}{BD}[/tex] ( cross- multiply )
DB² = 64 ( take the square root of both sides )
DB = [tex]\sqrt{64}[/tex] = 8
The length of segment DB is 8 units.
From the given right triangle we can deduce the following;
triangle ABD and triangle DBC are similar triangleslength AC = 17.8 unitslength AD = 5 unitsFrom the corresponding triangle rules, we can calculate the length of DB by considering the following ratios;
[tex]\frac{DB}{DC} = \frac{AD}{DB} \\\\DB^2 = AD\times DC\\\\DB^2 = 5 \times (17.8-5)\\\\DB^2 = 5 \times 12.8\\\\DB^2 = 64\\\\DB = \sqrt{64} \\\\DB = 8 \ units[/tex]
Thus, the length of segment DB is 8 units.
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