Question

Need help ASAP
questions in the pics i have sent

Answer 1

Explanation:

Picture 1

In right triangle ABC,

Side AB is the opposite side of angle C.

Picture 2

In triangle MKL,

tan(∠M) =
`\frac{\text{Opposite side}}{\text{Adjacent side}}`

=
`(KL)/(KM)`

=
`(15)/(8)`

Option (1) is the answer.

Picture 3

In ΔXYZ,

sin(∠Z) =
`\frac{\text{Opposite side}}{\text{Hypotenuse}}`

=
`(XY)/(XZ)`

For the length of XY we will apply Pythagoras theorem in ΔXYZ,

XZ² = XY² + YZ²

XY² = XZ² - YZ²

= (40)² - (32)²

XY = √576

= 24

sin(Z) =
`(24)/(40)`

sin(Z) =
`(3)/(5)`

Picture 4

In right triangle DEF,

Cos(D) =
`\frac{\text{Adjacent side}}{\text{Hypotenuse}}`

=
`(EF)/(DF)`

=
`(75)/(72)`

=
`(25)/(24)`

Picture 5

In ΔABC,

tan(63°) =
`\frac{\text{Opposite side}}{\text{Adjacent side}}`

tan(63°) =
`(BC)/(AB)`

AB =
`\frac{BC}{\text{tan}(63)}`

AB =
`\frac{8}{\text{tan}(63)}`

AB = 4.0762 ≈ 4 m

Option (3) will be the answer.