Question

I need help on these questions please

Answer 1

Answer:

Step-by-step 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°) = $\frac{12}{x}$

    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) = $\frac{20}{58}$

    x = $\text{tan}^{-1}(\frac{20}{58} )$

    x = 19.03

    x ≈ 19.0°

4). By applying cosine ratio in ΔJKF,

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

    tan(70) = $\frac{60}{x}$

    x = $\frac{60}{\text{tan}(70)}$

    x = 21.838

    x ≈ 21.8