  # Find an Angle Using the Sin Ratio

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

Why is this person hanging upside down?

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

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 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

Example 2 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

Over to you...

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