Question

Use trig ratios to find the measure of the angle in this Triangle (Image)

Answer 1

θ = 36.9°

Explanation:

Trigonometric ratios in a right triangle will be,

Sinθ =
`\frac{\text{Opposite side}}{\text{Hypotenuse}}` =
`\frac{\text{AC}}{\text{AB}}`

Cosθ =
`\frac{\text{Adjacent side}}{\text{Hypotenuse}}` =
`\frac{\text{BC}}{\text{AB}}`

Tanθ =
`\frac{\text{Opposite side}}{\text{Adjacent side}}` =
`\frac{\text{AC}}{\text{BC}}`

In the picture attached,

Given sides are,

AB = 5 and BC = 4

Therefore, to find the given angle θ only Cosine will be applicable.

Cos θ =
`\frac{\text{BC}}{\text{AB}}`

=
`(4)/(5)`

θ =
`Cos^(-1)(0.8)`

θ = 36.87°

θ ≈ 36.9°