a. θ = 36. 9°
b. θ = 114. 2°
How to determine the value of theta
a. We use the cosine identity
cos θ = adjacent/hypotenuse
Adjacent = 4cm
Hypotenuse = 5cm
cos θ = 4/ 5
cos θ = 0. 8
Now, we have the inverse of the cosine value
θ = cos^-1 (0. 8)
θ = 36. 9°
b. We use the tangent identity
tan a = opposite / adjacent
tan a = 3. 8/1. 7
tan a = 2. 23
a = tan^-1 ( 2. 23)
a = 65. 8
We have;
a + θ = 180 °; angles on a straight line
θ = 180 - 65. 9
θ = 114. 2°
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