Question

in the triangle abc the the foot of the perpendicular from a to b c is d given that tan b = 4 by 3 cos c equal to 15 by 17 and that AB = 220 CM calculate without using table the length of the sides AC and BC the value of sin a​

Answer 1

Answer:

In right angled triangle ∆ABD tanB=4/3

so BD= 3x , AD=4x

so, √(3x)^2+(4x)^2=220

5x=220

x=44

BD=132cm

AD= 176cm

In right angled triangle ∆ADC cosC= 15/17

so DC=15k and AC=17k

AC^2-DC^2=AD^2

17k^2-15k^2= 176^2

k^2=88*176

k=88√2

so, AC=17*88√2

DC=15*88√2

S

Hence BC = BD+DC= 132+15*88√2

Now sinA= Sin (angle BAD) + Sin(angle CAD)

= 126/85

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