Question

Type the correct answer in each box. If necessary, use/for the fraction bar(s).

In this triangle, the product of Sin B and tan C is_____, and the product of sin C and tan B is_____.

please view picture at the top

Answer 1

Answer:

1). sinB × tanC = $\frac{c}{a}$

2).  sinC × tanB = $\frac{b}{a}$

Step-by-step explanation:

From the figure attached,

A right triangle has been given with m∠A = 90°, m(AC) = b, m(AB) = c and m(BC) = a

SinB  = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

         = $\frac{\text{AC}}{\text{BC}}$

         = $\frac{b}{a}$

tanB = $\frac{\text{Opposite side}}{\text{Adjacent side}}$

        = $\frac{\text{AC}}{\text{AB}}$

        = $\frac{b}{c}$

SinC = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

        = $\frac{\text{AB}}{\text{BC}}$

        = $\frac{c}{a}$

tanC = $\frac{\text{Opposite side}}{\text{Adjacent side}}$

        = $\frac{c}{b}$

Now sinB × tanC = $\frac{b}{a}\times \frac{c}{b}$

                            = $\frac{c}{a}$

And sinC × tanB = $\frac{c}{a}\times \frac{b}{c}$

                           = $\frac{b}{a}$

Answer 2

Answer:

1). sinB × tanC =

2).  sinC × tanB =

Step-by-step explanation:

From the figure attached,

A right triangle has been given with m∠A = 90°, m(AC) = b, m(AB) = c and m(BC) = a

SinB  =

        =

        =

tanB =

       =

       =

SinC =

       =

       =

tanC =

       =

Now sinB × tanC =

                           =

And sinC × tanB =