22 min read
Finding Missing Angles
Use the inverse trig functions to find an angle when you know two sides.
Inverse Trig Functions
When you know two sides of a right-angled triangle, work out the ratio first (a decimal), then apply the inverse function on a calculator to find the angle.
Example 1 — easy numbers
A right-angled triangle has Opposite = , Hypotenuse = . Find the angle θ.
- Work out the ratio: sin(θ) =
- Apply the inverse function: θ = sin⁻¹() = °
Answer: °
Example 2 — using tan
A right-angled triangle has Opposite = , Adjacent = . Find the angle θ.
- Work out the ratio: tan(θ) =
- Apply the inverse function: θ = tan⁻¹() = °
Answer: °
Example 3 — a decimal answer
A right-angled triangle has Adjacent = , Hypotenuse = . Find the angle θ, to decimal place.
- Work out the ratio: cos(θ) = ≈
- Apply the inverse function: θ = cos⁻¹() ≈ °
Answer: ≈ °
Practice
A right-angled triangle has Opposite = , Adjacent = . Find the angle θ, to decimal place (in degrees).
Your answer
More lessons in Trigonometry · Next: Angles of Elevation and Depression · Previous: Finding Missing Sides