Find a Missing Side Using the Sin Ratio

 Question

What do the following have in common?

A triangle, a tricycle, a triathlete, trigonometry.

Answer

The number three.  Three sides on a triangle, three wheels on a tricycle, three events in a triathlon and 3 ratios to learn in trigonometry.

Ah yes, trigonometry 

Now you may be baffled by the different ratios (SOH, CAH, TOA) and when to multiply and divide.

We are going to look at Sin here.  

We can use sin to help us find the missing side in a right angled triangle.

A formula triangle is helpful.  The stuff in the triangle is going to help us.

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 side it is we want to find 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 opposite side, cover up the O.  The formula we are left with is Sin(angle) x Hypotenuse.

If we want to find the hypotenuse, cover up the H.  The formula we are left with is opposite (O) divided by Sin(angle)

 Let's give it a go.

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

Example 1

1. Label the triangle

2. Find the two sides you want.  You want to find x, so we want H, and the only other side you have to help is the O.

3. Look at your formula triangle, cover up the side you want to find, which is H. (see above)

4.  We are left with O ÷ sin 38

5. In your calculator type in 5 ÷ sin 38

6. Your answer should be 8.12 cm to 2 decimal places.

Example 2

1. Label your triangle

2. Find the sides you want

3.  You should have discovered you wanted H and O

4. Use your formula triangle and cover up O the side you want to find

5. The formula you are left with is Sin 27 x 10 = 4.54 to 2 decimal places

Don't you think it quite fitting that a trigonometry question has a formula triangle to help us?