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 Hard
Hard
(Originais Teachy 2024) - Question Hard of Mathematics
During the cleaning of the cooling system of a factory, a technician must adjust a light reflector fixed on the ceiling of the room. The reflector has the shape of a right circular cone with the vertex pointing upwards and an opening angle of 75º. The technician wants to calculate the height and the radius of the base of the cone to determine the ideal dimensions of the mirrors that will be installed on the inner surface of the cone, so that the reflected light follows a beam parallel to the floor. Consider that the angle of incidence of light on the inner surface of the cone should be 15º with the normal to the surface at the point of incidence to ensure total reflection of light. Based on this configuration, determine the height and the radius of the base of the cone, and additionally, identify the value of the sine and cosine of 22.5º, an angle that arises in the resolution of the problem.a.
Height h ≈ 0.1392 and base radius r ≈ 0.0927. Sine of 22.5º ≈ 0.6614 and cosine of 52.5º ≈ 0.5000.
b.
Height h ≈ 0.1392 and base radius r ≈ 0.0927. Sine of 22.5º ≈ 0.5000 and cosine of 52.5º ≈ 0.6614.
c.
Height h ≈ 0.1392 and base radius r ≈ 0.0927. Sine of 22.5º ≈ 0.6614 and cosine of 52.5º ≈ 0.5000.
d.
Height h ≈ 0.0927 and base radius r ≈ 0.1392. Sine of 22.5º ≈ 0.6614 and cosine of 52.5º ≈ 0.5000.
e.
Height h ≈ 0.0927 and base radius r ≈ 0.1392. Sine of 22.5º ≈ 0.5000 and cosine of 52.5º ≈ 0.6614.
Answer sheet:
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