Question

In the right angle ∆abc, B= 90° if tan c=13 the value of the angle A it's

Answer 1

Answer:

wait 6 mins

Step-by-step explanation:

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