Question

Angles. Maybe using law of sines

Answer 1

Answer:

(a) 5.36°

(b) β = 84.64° -θ

(c) d = 58.36·sin(84.64° -θ)/sin(θ)

(d) see the attached table

Step-by-step explanation:

(a) The lean angle can be found from the definition of the sine function:

sin(α) = Opposite/Hypotenuse = (5.45 m)/(58.36 m) ≈ 5.36°

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(b) The angle β does not depend on d; it only depends on the angle θ. Since the sum of angles of a triangle is 180°, we have ...

θ + (90°+α) + β = 180°

β = 180° -90° -5.36° -θ

β = 84.64° - θ

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(c) The law of sines tells you ...

d/sin(β) = 58.36/sin(θ)

Using the above expression for β and multiplying by sin(β), we get ...

d = 58.36·sin(84.64° -θ)/sin(θ)

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This can be simplified, if desired, to ...

d = 58.10·cot(θ) -5.45