The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Find an Angle Using the Sin Ratio

In this worksheet, students will use the Sin ratio to find the missing angle of a triangle.

'Find an Angle Using the Sin Ratio' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation, Triangle Mensuration

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

 

person hanging upside down

Question

Why is this person hanging upside down?

Answer

To look at something in a slightly different way.

 

We know that anything starting with the letters tri, means three things.

Three sides on a triangle, three wheels on a tricycle, three events in a triathlon and three ratios to learn in trigonometry.

 

Ah yes, our favourite trigonometry 

 (SOH, CAH, TOA) 

You may have used the formula triangle to help find a missing side of a right angled triangle.

We can use  also them to help us find the missing angle in a right angled triangle.

 

Here we are going to look at the Sin formula triangle.

 We will use it the same way as when finding a missing side, except for something slightly different at the end.

 

S is for SIN (which will be given as an angle)

O is for opposite side from the angle

H is the hypotenuse

The line in the middle means divide.

To use this triangle we cover up what it is we want to find (sin means angle) and we are left with a formula to follow.

The good old formula, where would we be without it.

sin ratio

If we want to find the angle, The formula we are left with is opposite ÷ hypotenuse.

writing Let's give it a go.

IMPORTANT NOTE: Make sure your calculator is set to degrees. You can tell as a D appears at the top of the screen.

Example 1

sin find angle

1. Label the triangle. 

2. Find the two sides you want.  You want to find the angle, the only information to help us is the length of the hypotenuse H, and the length of the opposite side O.

3. Look at your formula triangle, cover up Sin (meaning angle)(see above)

4.  We are left with O ÷  H

5. In your calculator type in 3 ÷ 7 = 0.42. This is clearly not correct.

This is where the slight difference occurs.  You use the inverse sin button  (sin -1)on your calculator.  This is the upside down bit.

You usually access this by pressing shift and then sin

Your answer should be 25.38° to 2 decimal places.

 

Example 2

sin ratio angle

 

1. Label the triangle

2. Find the two sides you want.  You want to find the angle, the only information to help us is the length of  H, and the length of O.

3. Look at your formula triangle, cover up Sin (meaning angle)(see above)

4.  We are left with O ÷  H

5. In your calculator type in 5 ÷ 8 = 0.625.

This is where the slight difference occurs.  You use the inverse sin button  (sin -1)on your calculator.  

You usually access this by pressing shift and then sin

Your answer should be 38.68° to 2 decimal places.

 

 

Over to you..

sin ratio angle

Find the angle in this triangle.

Answer has been rounded to 2 decimal places

41.81°

52.43°

38.21°

55.55°

sin ratio find angle

Find the size of the angle

Round your answer to 1 decimal place.

Write your answer in figures without the units.

 

 

 

 hypotenuse ÷ oppositeopposite ÷ hypotenuse42.42°36.87°40.12 °
The formula I need is
The angle is

sin ratio angle

Round your answer to 2 decimal places (2 d.p)

 hypotenuse ÷ oppositeopposite ÷ hypotenuse42.42°36.87°40.12 °
The formula I need is
The angle is

sin ratio angle

 

Round your answer to 2 decimal places (2 d.p)

34.98°

44.38°

64.28°

54.18°

Sin ratio angle

Round your answer to 2 decimal places.

Write your answer in figures without the units.

 

sin ratio angle

 

 62.73°63.37°64.46°
The angle is

sin ratio angle

Round your answer to 2 decimal places (2 d.p)

 62.73°63.37°64.46°
The angle is

sin ratio angle

Find the size of the angle

Round your answer to 2 decimal places (2 d.p).

Write your answer in figures without the units.

sin ratio angle

Answer has been rounded to 2 decimal places (2 d.p)

43.81°

45.32°

48.29°

47.62°

  • Question 1

sin ratio angle

Find the angle in this triangle.

Answer has been rounded to 2 decimal places

CORRECT ANSWER
41.81°
EDDIE SAYS
To find an angle, you are always going to need the opposite and the hypotenuse, but it can be easy to get the opposite and adjacent muddled up when there are measurements on all sides of the triangle. So care labelling is needed. Here you are given the opposite and hypotenuse only, so there is little room for error. 8 ÷ 12 = 0.66 0.66 sin-1 = 41.81 (to 2 d.p)
  • Question 2

sin ratio find angle

Find the size of the angle

Round your answer to 1 decimal place.

Write your answer in figures without the units.

CORRECT ANSWER
56.4
EDDIE SAYS
opposite ÷ hypotenuse 5 ÷ 6 = 0.8333 0.8333 Sin-1 = 56.4 sin sational!!
  • Question 3

 

 

 

CORRECT ANSWER
 hypotenuse ÷ oppositeopposite ÷ hypotenuse42.42°36.87°40.12 °
The formula I need is
The angle is
EDDIE SAYS
Labelling the triangle correctly is key to unlocking he correct formula, particularly here when you have all three sides labelled. You know you need the opposite divided by the hypotenuse 9 ÷ 15 = 0.6 sin-1 0.6 = 36.87 to 2 decimal places
  • Question 4

sin ratio angle

Round your answer to 2 decimal places (2 d.p)

CORRECT ANSWER
EDDIE SAYS
How are you getting on using the formula triangle? It is easier when finding the angle as the formula comes out the same each time. O ÷ H 18 ÷ 22 = 0.8181 sin-1 0.8181 = 54.90° sin tillating stuff huh?
  • Question 5

sin ratio angle

 

Round your answer to 2 decimal places (2 d.p)

CORRECT ANSWER
54.18°
EDDIE SAYS
Are you getting used to this now? 15 ÷ 18.5 =0.8108 sin-1 0.8108 = 54.18°
  • Question 6

Sin ratio angle

Round your answer to 2 decimal places.

Write your answer in figures without the units.

CORRECT ANSWER
43.81
EDDIE SAYS
Are you on a roll now. 4.5 ÷ 6.5 = 0.6923.. sin-1 0.6923... = 43.81° (to 2 d.p) Have you noticed that all angles come out as acute angles. If you have got anything over 90° then you have made a mistake somewhere.
  • Question 7

 

sin ratio angle

 

CORRECT ANSWER
 62.73°63.37°64.46°
The angle is
EDDIE SAYS
To be honest once you can label your triangle correctly you can leave the rest to your scientific calculator. What a great friend it is at a time like this. 8 ÷ 9 = 0.888 sin-1 0.888 = 62.73°
  • Question 8

sin ratio angle

Round your answer to 2 decimal places (2 d.p)

CORRECT ANSWER
EDDIE SAYS
Calculators rock. The only thing you have to be careful of, is rounding to the correct number of decimal places. 10 ÷18 = 0.555 sin-1 0.555 = 33.75 (to 2 d.p)
  • Question 9

sin ratio angle

Find the size of the angle

Round your answer to 2 decimal places (2 d.p).

Write your answer in figures without the units.

CORRECT ANSWER
48.59
EDDIE SAYS
Whaaaat -this isn't a right angled triangle. What do I do now? You must have been waiting for the curved ball. Just turn it into one by drawing a line from the vertex to the opposite side. Don't forget to halve the base to give the correct length for the opposite side. Nearly there. I hope you haven't found this to tri-ing!! 4.5 ÷ 6 = 0.75 sin -1 0.75 = 48.59° (to 2 d.p)
  • Question 10

sin ratio angle

Answer has been rounded to 2 decimal places (2 d.p)

CORRECT ANSWER
43.81°
EDDIE SAYS
Are you ready to sin out now? One final check though 4.5 ÷ 6.5 = 0.6923... sin-1 0.6923 = 43.81(to 2 d.p)
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started
laptop

Start your £1 trial today.
Subscribe from £10/month.