3D Trigonometry

3D trigonometry is a branch of mathematics that uses principles from RightAngle Trigonometry and Pythagoras’ Theorem to solve problems involving threedimensional shapes.

It’s pivotal to know the basic 2D trigonometric ratios: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, and tan θ = opposite/adjacent. These principles are equally applicable in 3D trigonometry.

In 3D problems, one must first identify the rightangled triangle involved.

Another necessary element to understand is the rightangled triangle’s sides: the opposite (perpendicular to the angle), the adjacent (next to the angle and the right angle), and the hypotenuse (the longest side opposite the right angle).

The threedimensional version of Pythagoras’ Theorem can be used to find the length of a line segment in a threedimensional space. If the segment has endpoints with coordinates (x1, y1, z1) and (x2, y2, z2), then the length of the segment is √[(x2 − x1)^2 + (y2 − y1)^2 + (z2 − z1)^2].

3D Trigonometry is commonly used to solve real life problems such as finding the angles between intersecting lines or planes, the height of a tall object from a certain distance and angle of elevation, or establishing the shortest distance between two points in 3D space.

It is important to practise 3D trigonometry problems. Visualizing the problem or using models can help with understanding.

Always check the results. If the angles do not add up to 180 degrees or if the sides do not satisfy Pythagoras’ theorem in a right angled triangle, then the answer is likely incorrect.

Past problem sets filled with 3D Trigonometryrelated questions will often help with grasping the principles better. Do ensure regular practise to solidify your understanding and improve speed during assessments.

3D Trigonometry is often tested in conjunction with other topics, such as geometry, algebra and problemsolving, so a solid grasp of these areas can also be beneficial.