Trigonometry

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• Middelbare school
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• Leerjaar 3

6.1 & 6.2

Angle of Elevation

Gradient

Tangent

In Chapter 6 - Trigonometry

When you have a right-angled triangle you can use the trigonomic ratios tangent, sine and cosine to calculate the length of a side or the size of an angle.

SOH CAH TOA

When writing your answer please try to use the following :

Regel

Invullen

Antwoord

Also remember:

How to calculate the length of a side or angle in a right-angled triangle

- make a sketch 

- include all known data (opposite, hypotenuse and adjacent sides)

- write down what you know and what you are trying to calculate so that you can use SOH CAH TOA to choose which ratio to use

- write down the ratio and fill in what you know

- calculate the answer

when to use tan or shift tan?

Use  tan, sin and cos when you know the angle.

Use shift tan, shift sin and shift cos when you know the ratio of lengths of sides and you want to calculate the angle

Sine and Cosine

VWO: ex 15 t/m 20 on pages 200 t/m 202

HAVO: ex 21 t/m26 on pages 210 t/m 212

Calculating in right-angled triangles

VWO: ex 21 t/m 26 on pages 204 t/m 206

HAVO: ex 27 t/m 32 on pages 214 t/m 216

How to make a right-angled triangle by drawing an auxillary line

In a triangle that has no right-angle you first have to draw an auxillary line to make a right-angled triangle. You do this by drawing a line perpendicular to a side and passing through the opposite vertex.

How to calculate an angle between two line segments in a solid

Look for a cross-section in which both line segments lie

Make a sketch of this cross-section and include all known date.

Check if you can calculate the angle. Sometimes you have to calculate the length of a line segment first.

Calculate the angle. Do not round the intermediate answers.

Which ratio do you use to calculate the angle of elevation?

Practise exercises

Mixed Exercises 

Test Yourself 

Extra exercises

Do you have any questions?