From a certain point you can see two ends of one side of a square; the angle formed between the imaginary lines that go towards both ends and whose vertex is the observation point is 56 °. The distances from the observation point to the extremes are 71 and 58 meters, respectively.
Respuestas
Respuesta:
Triangle, Vertex, Angle, Observation Point, Square.
Data:
Observation angle = 56 °
Distance 1 = 71 m
Distance 2 = 58 m
For a better understanding, analysis and solution of the problem, the diagram in the attached figure is proposed. (view image)
Since it does not indicate what to calculate, then the length of the side of the square (L) and the missing angles will be calculated.
To do this, the median (m) is imagined from the vertex of the observation point next to the square, which causes a right triangle to form between it; the observation point and the middle of the side of the square, which can be solved by the Law of Sines.
71 m / Sen 90 ° = (L / 2) / Sen (56/2) = m / Sen β
Clears (L / 2)
L / 2 = 71 m (Sen 28 / Sen 90 °) = 33.33 m
L / 2 = 33.33 m
Consequently, the length of L is.
L = 2 x 33.33 m = 66.66 m
L = 66.66 m
By theory it is known that the sum of the internal angles of a triangle is 180 °.
180 ° = 90 ° + 28 ° + β
β = 180 ° - 90 ° + 28 ° = 62 °
β = 62 °
Then the angle alpha (α) is:
α = 180 ° - 56 ° - 62 ° = 62 °
α = 62 °
Explicación paso a paso: