in the right angle .angle abc, b=90. if tan root 3, the value of the angle a is
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Answer:
right angled Δ ABC,
Given, tanC= 3
We know that, tanθ=
adjacent side to∠θ
opposite side to∠θ
∴AB= 3and AC=1
From Pythagoras theorem,
BC 2
=AB 2 +AC 2
BC 2
=( 3 ) 2+1 2
BC 2=3+1=4
BC=2
sinθ=
hypotenuse
opposite side to∠θ
cosθ= hypotenuse
adjacent side to∠θ
sinB= BC
AC
= 21
cosB= BC
AB
= 23
sinC= BCAB = 23
cosC=BCAC
= 21
Therefore,
sinBcosC + cosBsinC
=( 21 )( 21 ) + ( 23 )( 23 )
= 41 +43=44
=1
Step-by-step explanation:
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