1. In the figure ∠ CDB = φ , ∠ ACB = θ
∠ ABC = 90° find the values of
a) sin θ
b) 4 (tan θ - sin φ )
Answers
Answered by
0
Step-by-step explanation:
Given, BD = 8 cm, AD = 4 cm, ZABC = 90° and BD LAC.
we know that,If a perpendicular is drawn from the vertex containing a right angle of a right triangle to the hypotenuse then the triangle on each side of the perpendicular are similar to each other and to the whole triangle.
So, ADBA ~ ADCB (A-A similarity)
BD/CD = AD/BD
[Since, triangles are similar, hence corresponding sides will be proportional]
B * D ^ 2 = ADDC
(8) ^ 2 = 4DC
64 = 4DC
DC = 64/4
DC = 16
Hence, the length of CD is 16 cm..
Answered by
11
Answer:
In the given figure,
∠C=90
∘
In △ABC,
tan∠ABC=
B
P
=
BC
AC
In △CDB,
tan∠DBC=
B
P
=
BC
CD
Now,
tan∠DBC
tan∠ABC
=
BC
CD
BC
AC
tan∠DBC
tan∠ABC
=
CD
AC
tan∠DBC
tan∠ABC
=
CD
2CD
tan∠DBC
tan∠ABC
=2 (D is mid point of AC)
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