Question about Trigonometric Lines of 75º, 15º, 22.5º
Subject Mathematics
Mathematics
Source Originais Teachy
Originais Teachy
Topic Trigonometric Lines of 75º, 15º, 22.5º
Trigonometric Lines of 75º, 15º, 22.5º
Difficulty Easy
Easy
(Originais Teachy 2024) - Question Easy of Mathematics
In an engineering project, a beam of light needs to be directed so that it strikes a reflective surface at an angle of 75º in relation to the normal of that surface, in order to avoid dazzling operators who will be handling parts in the same environment. The light initially strikes perpendicular to the ceiling, and a mirror placed at 15º in relation to this light source will reflect it in the desired direction. Additionally, it is necessary to install a prism with an angle of 22.5º so that the light coming out of the mirror reaches the reflective surface with the correct inclination. Considering only the action of the mirror and the prism on the direction of the light beam, calculate the angle at which the light exits the mirror and the additional rotation that the light beam undergoes when passing through the prism.a.
The light exits the mirror at an angle of 90º in relation to its surface, and after passing through the prism, the direction of the light beam is rotated by 15º.
b.
The light exits the mirror at an angle of 15º in relation to its surface, and after passing through the prism, the direction of the light beam remains unchanged, without additional rotation.
c.
The light exits the mirror at an angle of 75º in relation to its surface, and after passing through the prism, the direction of the light beam is rotated by 30º.
d.
The light exits the mirror at an angle of 30º in relation to its surface, and after passing through the prism, the direction of the light beam is rotated by 75º.
e.
The light exits the mirror at an angle of 15º in relation to its surface, and after passing through the prism, the direction of the light beam is rotated by 45º.
Answer sheet:
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Answer sheet
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