MathsFreePrintable

Right-Angled Triangle Solutions

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Download now

Name:Date:

Right-Angled Triangle Solutions

Use a calculator in degree mode. Choose sine, cosine or tangent to connect the sides you know to the side or angle you need. Give lengths to 1 decimal place unless asked otherwise, and show your working.

Choose your ratio

Label the sides opposite, adjacent and hypotenuse in relation to the marked angle.

1.A right-angled triangle has an angle of 32°. The side opposite this angle is 7 cm. Which ratio will find the hypotenuse?

Sine
Cosine
Tangent

2.A right-angled triangle has an angle of 40° and an adjacent side of 9 cm. Calculate the opposite side. Give your answer to 1 decimal place.

3.A right-angled triangle has a hypotenuse of 14 m and an angle of 53°. Find the adjacent side, to 1 decimal place.

4.The side opposite a 28° angle is 6 cm. Calculate the hypotenuse, to 1 decimal place.

Find the missing angle

Use an inverse trigonometric function, such as sin⁻¹, cos⁻¹ or tan⁻¹.

5.In a right-angled triangle, the opposite side is 5 cm and the hypotenuse is 13 cm. Find the angle opposite the 5 cm side, to 1 decimal place.

6.The opposite side of an angle is 8.4 m and its adjacent side is 11 m. Find the angle to the nearest degree.

Put trigonometry to work

Sketch a right-angled triangle for each situation and mark the angle and measurements before choosing a ratio.

7.A 6 m ladder rests against a vertical wall. Its foot is 2 m from the wall. What angle does the ladder make with the ground? Give your answer to the nearest degree.

8.A surveyor stands 30 m from the base of a tower. The angle of elevation from the ground to the top is 35°. Estimate the tower's height to 1 decimal place. Assume the ground is level.

9.A wheelchair ramp rises 0.75 m over a horizontal distance of 8 m. What angle does the ramp make with the horizontal? Give your answer to 1 decimal place.

10.A kite is 18 m above the ground. The angle of elevation from a point on level ground to the kite is 42°. How far is that point from the spot directly below the kite? Give your answer to 1 decimal place.

3 printable pages

Page 1
Page 2
Page 3

Download now

About This Worksheet

Free in Kuraplan

Print-Ready

Formatted for standard paper. Clean layout, easy to read.

AI-Generated

Created with Kuraplan's AI, designed for real classroom use.

For Teachers & Parents

Use in classrooms, for homework, tutoring, or homeschool.

Need a custom version of this worksheet?

Kuraplan's AI generates custom worksheets in seconds — differentiated for every learner, aligned to your curriculum.

Generate Custom Worksheets — Free

No credit card Curriculum-aligned Under 60 seconds

More Maths Worksheets

Right-Angled Triangle Solutions

Right-Angled Triangle Solutions

Choose your ratio

Find the missing angle

Put trigonometry to work

3 printable pages

About This Worksheet

Free in Kuraplan

Print-Ready

AI-Generated

For Teachers & Parents

Need a custom version of this worksheet?

More Maths Worksheets

GCSE Bearings Practice Worksheet

Circle Circumference Practice Worksheet

3D Shapes Classification Worksheet

Drawing Polygons Practice

Exploring Polygons Worksheet

Shape Pattern Rules

SOH-CAH-TOA Practice Worksheet

Angles and Parallel Lines

Explore more free resources