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

1). sinB × tanC =
`(c)/(a)`

2). sinC × tanB =
`(b)/(a)`

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}}`

=
`(b)/(a)`

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

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

=
`(b)/(c)`

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

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

=
`(c)/(a)`

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

=
`(c)/(b)`

Now sinB × tanC =
`(b)/(a)* (c)/(b)`

=
`(c)/(a)`

And sinC × tanB =
`(c)/(a)* (b)/(c)`

=
`(b)/(a)`