Explanation:
A good trick to remember is SOH CAH TOA.
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
I'll do the bottom row as an example.
In the first triangle, the hypotenuse is x. The side opposite of the 30° angle is 13 cm. Since we have opposite and hypotenuse, we'll use sine.
sin 30° = 13 / x
x = 13 / sin 30°
x = 26
In the second triangle, the hypotenuse is 15 cm. The side adjacent to the 45° angle is x. Since we have adjacent and hypotenuse, we'll use cosine.
cos 45° = x / 15
x = 15 cos 45°
x ≈ 10.61
In the third triangle, the hypotenuse is 15 cm. The side opposite of θ is 7 cm. Since we have opposite and hypotenuse, we'll use sine.
sin θ = 7 / 15
θ = sin⁻¹ (7/15)
θ ≈ 27.82°
In the fourth triangle, the side opposite of θ is 6 cm, and the side adjacent to θ is 15 cm. Since we have opposite and adjacent, we'll use tangent.
tan θ = 6/15
θ = tan⁻¹ (6/15)
θ ≈ 21.80°