Step-by-step explanation:
Use SOH-CAH-TOA.
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
For example, in 2(a), we are given an angle and the hypotenuse. We want to find the side adjacent to the angle. Therefore, we should use cosine.
cos 58° = y / 32.3
y = 32.3 cos 58°
y ≈ 17.1
In 3(a), we are given the adjacent side and opposite side. We want to find the angle. So use tangent.
tan θ = 3.6 / 6.2
θ = tan⁻¹(3.6/6.2)
θ = 30.1°
In 4(a), we are given an angle and the hypotenuse. We want to find the side opposite of the angle. Therefore, we should use sine.
sin 47° = x / 29
x = 29 sin 47°
x ≈ 21.2