Calculating an angle
Check out the updated revision resources for GCSE Maths: Calculating an angle, with step-by-step slideshows, quizzes, practice exam questions, and more!
The three trigonometric ratios can be used to calculate the size of an angle in a right-angled triangle.
Example
Calculate the angle QPR. Give the answer to one decimal place.
Label the sides of the triangle \(o\), \(a\) and \(h\).
Next choose the correct ratio from \(s^o_h~c^a_h~t^o_a\).
In the triangle the lengths \(o\) and \(a\) are known.
Use: \(\tan{x} = \frac{o}{a}\)
\(\tan{x} = \frac{5}{7}\)
To calculate the angle use the inverse tan button on the calculator (\(\tan^{-1}\))
\(x = \tan^{-1} (\frac{5}{7})\)
\(x = 35.5^\circ\)
Question
Calculate the angle KJL. Give the answer to one decimal place.
Label the sides of the triangle \(o\), \(a\) and \(h\).
Next choose the correct ratio from \(s^o_h~c^a_h~t^o_a\).
In the triangle the lengths \(a\) and \(h\) are known.
Use: \(\cos{x} = \frac{a}{h}\)
\(\cos{x} = \frac{4}{6}\)
To calculate the angle use the inverse cos button on the calculator (\(\cos^{-1}\))
\(x = \cos^{-1} (\frac{4}{6})\)
\(x = 48.2^\circ\)
More guides on this topic
- NEW: Angles
- NEW: Angles in parallel lines
- NEW: Polygons
- NEW: Line and rotational symmetry
- NEW: Constructing triangles
- NEW: Ruler and compass constructions
- NEW: Loci
- NEW: Bearings
- NEW: Perimeter
- NEW: Area
- NEW: Volume of a prism
- NEW: Surface area of a prism
- NEW: Pyramids, cones and spheres
- NEW: Nets, plans and elevations
- NEW: Circumference and arc length
- NEW: Area of circles and sectors
- NEW: Higher – Circle Theorems – Calculating angles using circles
- NEW: Higher – Using the alternate segment theorem, tangents and chords
- NEW: Reflection
- NEW: Rotation
- NEW: Translation
- NEW: Enlargement
- NEW: Higher − Negative enlargements
- NEW: Higher – Combined transformations and invariant points
- NEW: Congruent and similar shapes
- NEW: Higher – Similarity in 2D and 3D shapes
- NEW: Pythagoras' theorem
- NEW: Solving 2D and 3D problems using Pythagoras' theorem
- NEW: Right-angled trigonometry
- NEW: Exact trigonometric values
- NEW: Higher – Sine rule – OCR
- NEW: Higher – Cosine rule
- NEW: Higher – 2D and 3D trigonometry problems
- NEW: Vectors
- NEW: Higher – Geometric problems using vectors
- Angles, lines and polygons - OCR
- Loci and constructions - OCR
- 2-dimensional shapes - OCR
- 3-dimensional solids - OCR
- Circles, sectors and arcs - OCR
- Circle theorems - Higher - OCR
- Transformations - OCR
- Pythagoras' theorem - OCR
- Units of measure - OCR
- Vectors - OCR
