in the right triangle abc angle B = 90 degree if tan C = root 3 the value of the angle A is
Answers
Answer:
In right angled Δ ABC,
Given, tanC=
3
We know that, tanθ=
adjacent side to∠θ
opposite side to∠θ
∴AB=
3
and 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
=
2
1
cosB=
BC
AB
=
2
3
sinC=
BC
AB
=
2
3
cosC=
BC
AC
=
2
1
Therefore,
sinBcosC + cosBsinC
=(
2
1
)(
2
1
) + (
2
3
)(
2
3
)
=
4
1
+
4
3
=
4
4
=1
solution
Answer:
30 degree
Step-by-step explanation:
In triangle ABC, angle B=90 degree
tan c=root 3
tan c = opposite/ adjacent
tan c= root3
tan c= 60degree. (because in introduction to trigonometry chapter class 10 table box)
We know that,
angleA + angleB + angle c= 180 degree
angleA + 90degree + 60 degree= 180 degree
angle A + 150 degree = 180 degree
angle A= 180 degree - 150 degree
angle A = 30 degree
