Question

I need help on these questions please

Answer 1

Explanation:

1). In ΔABC,

For angle A as a reference angle,

Opposite side of ∠A → BC

Adjacent side of ∠A → AC

Hypotenuse → AB

2). By using tangent ratio in ΔYWZ,

tan(72°) =
`\frac{\text{Opposite side}}{\text{Adjacent side}}`

tan(72°) =
`(12)/(x)`

x =
`\frac{12}{\text{tan}(72)}`

x = 3.899

x ≈ 3.9

3). By using sine rule in ΔKNM,

tan(x°) =
`\frac{\text{Opposite side}}{\text{Hypotenuse}}`

tan(x) =
`(20)/(58)`

x =
`\text{tan}^(-1)((20)/(58) )`

x = 19.03

x ≈ 19.0°

4). By applying cosine ratio in ΔJKF,

tan(70°) =
`\frac{\text{Opposite side}}{\text{Adjacent side}}`

tan(70) =
`(60)/(x)`

x =
`\frac{60}{\text{tan}(70)}`

x = 21.838

x ≈ 21.8