Why Is Trigonometry Important? Its Role in STEM Fields

Discover how one right-triangle shortcut helps engineers, scientists, builders, programmers, and healthcare professionals solve real problems.

The main idea: connect angles and sides

Trigonometry studies relationships among angles and side lengths. Its most useful beginner trick is SOHCAHTOA, a memory word for the three basic ratios in a right triangle. Once you identify the known angle, the known side, and the unknown side, you can choose the correct ratio and solve step by step.

Step 1: Learn SOHCAHTOA

Sine = Opposite ÷ Hypotenuse   |   Cosine = Adjacent ÷ Hypotenuse   |   Tangent = Opposite ÷ Adjacent

On a small phone screen, swipe horizontally inside the equation box if needed.

Opposite is across from the chosen angle. Adjacent touches the angle but is not the hypotenuse. The hypotenuse is always opposite the 90° angle and is the longest side.

Step 2: Choose the ratio

Use the ratio containing the two pieces of information you have. If the problem gives the opposite side and hypotenuse, use sine. If it gives adjacent and hypotenuse, use cosine. If it gives opposite and adjacent, use tangent.

Known pair: O and H → sine    A and H → cosine    O and A → tangent

Worked example 1: Find a missing height

Problem: A wheelchair ramp is 20 feet long and rises at an angle of 18°. How high does it rise?

Step 1: Label the sides. The ramp is the hypotenuse, and the rise is opposite the 18° angle.

Step 2: Choose sine. sin(18°) = opposite ÷ hypotenuse.

opposite = 20 × sin(18°) ≈ 20 × 0.3090 = 6.18 feet

Answer: The ramp rises approximately 6.18 feet.

Worked example 2: Find an angle

Problem: A drone is 120 feet horizontally from a launch point and 50 feet above it. What is its angle of elevation?

The vertical side is opposite the angle, and the horizontal side is adjacent. Use tangent:

tan(θ) = 50 ÷ 120 = 5 ÷ 12 ≈ 0.4167

θ = arctan(0.4167) ≈ 22.6°. So the angle of elevation is approximately 22.6°.

How trigonometry powers STEM

STEM field	Trigonometry in action
Engineering	Resolve forces, design bridges, and calculate slopes.
Physics	Model waves, motion, energy, and rotating systems.
Computer science	Build 3D graphics, robotics movement, and game physics.
Medicine	Interpret imaging, waves, and measurement signals.
Earth science	Estimate distances, slopes, heights, and directions.

On a phone, swipe horizontally inside the table to read every column.

Memory tip

“Some Old Hikers Caught Another Hiker Tripping.” The first letters remind you: Sine = Opposite over Hypotenuse, Cosine = Adjacent over Hypotenuse, and Tangent = Opposite over Adjacent.

Common mistakes

1. Calling a side “opposite” without first naming the reference angle.
2. Using the hypotenuse as an adjacent side. The hypotenuse is a special side and is never the ordinary adjacent side in SOHCAHTOA.
3. Forgetting to switch the calculator to degree mode when angles are given in degrees.
4. Rounding too early. Keep several decimal places until the final answer.
5. Using inverse tangent when the known sides are opposite and hypotenuse.

Practice questions

1. A right triangle has an angle of 30° and a hypotenuse of 14. Find the opposite side.
2. A right triangle has opposite side 8 and adjacent side 15. Find the angle to the nearest tenth of a degree.
3. Which ratio connects adjacent and hypotenuse?
4. A 10-foot ladder makes a 65° angle with the ground. How high up the wall does it reach?

Answers

1. Opposite = 14 × sin(30°) = 14 × 0.5 = 7.
2. θ = arctan(8 ÷ 15) = arctan(0.5333) ≈ 28.1°.
3. Cosine: cosine = adjacent ÷ hypotenuse.
4. Height = 10 × sin(65°) ≈ 10 × 0.9063 = 9.06 feet.

Final takeaway

Trigonometry is a translation tool. It turns an angle into useful information about distance, height, direction, force, or motion. The SOHCAHTOA shortcut is a small idea with a huge STEM footprint: label the triangle, choose the matching ratio, solve, and check whether the result makes sense.