Answer
a) Angle L = 36.9°
Angle N = 53.1°
b) For the relationship between them, we can see that
Angle L + Angle N = 36.9° + 53.1° = 90°
Hence, they both sum up to give 90° and are thus complementary angles.
Step-by-step explanation
In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
For this question, we first use Angle L as the non-right-angle angle
Hypotenuse = LN = 5
Opposite = NM = ?
Adjacent = LM = 4
Angle = L
Trignometric ratios allow us to interprete CAH as
Cos L = (Adj/Hyp)
Cos L = (4/5)
Cos L = 0.8
L = Cos⁻¹ (0.8)
L = 36.9°
Now, using Angle N as the non-right-angle angle,
Hypotenuse = LN = 5
Opposite = LM = 4
Adjacent = NM = ?
Angle = N
Trignometric ratios allow us to interprete SOH as
Sin N = (Opp/Hyp)
Sin N = (4/5)
Sin N = 0.8
N = Sin⁻¹ (0.8)
N = 53.1°
b) For the relationship between them, we can see that
Angle L + Angle N = 36.9° + 53.1° = 90°
Hence, they both sum up to give 90° and are thus complementary angles.
Hope this Helps!!!