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In the diagram below, BC is an altitude of AABD. To the nearest whole unit,
what is the length of CD?
B
30
A
O
16ο
Α. 52
Β. 58
C, 44
D. 56

In The Diagram Below BC Is An Altitude Of AABD To The Nearest Whole Unit What Is The Length Of CD B 30 A O 16ο Α 52 Β 58 C 44 D 56 class=

Sagot :

Answer:

56

Step-by-step explanation:

Let CD = x  and BD = y

In triangle ABC  [tex]AB^{2} = 16^{2} + 30^{2}[/tex] by the Pythagorean theorem.

So [tex]AB^{2} = 256 + 900 = 1156\\\\AB = \sqrt{1156} = 34[/tex]

Now in triangle ABD

[tex]AB^{2} + BD^{2} = AD^{2} \\\\34^{2} + y^{2} = (x + 16)^{2}[/tex] by the Pythagorean theorem

[tex]1156 + y^{2} = x^{2} + 32x + 256[/tex]

[tex]y^{2} = x^{2} + 32x - 900[/tex]

and in triangle ACD  [tex]30^{2} + x^{2} = y^{2}[/tex]  by the Pythagorean theorem

Now

[tex]y^{2} = x^{2} + 32x - 900 = 900 + x^{2} \\\\32x = 1800\\\\x = 56.25[/tex]

Balabedali939816idn

Answer:

Step-by-step explanation:

D

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