3Tvwo §6.6 Mixed exercises

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 3

§6.6 Mixed exercises

First of all:

a mistake in exercise B36c, p.213

Correct with a pencil:

B36c 'Show that angle LNM' should be:
'Show that angle LMN' !!

Some fine points of the exercises will be discussed now!

Studysquarers: 

you are invited to join in, but you also work out thsi § for yourself on the Study square.

You may skip the first two: 32 and 33.

about 32, first have a look:

A useful SKETCH:

How to find 32a: The height of the mast?

1. sin 35 degrees
2. cos 35 degrees
3. Pythagoras in ACD
4. tan 35 degrees

Answer explained:

 cos 35 degrees 

is needed here, because you know: 

the hypotenuse and you want to know:

the adjacent side!

For 32 b what could be a good plan?

Answer this in the next slide!

All you for need 32b is:

1. tan 35 degrees
2. Pythagoras in ACD and in BCD too
3. sin 35 degrees and Pythagoras in BCD
4. Pythagoras in BCD

Now about 33:

This is a Sketch for 33a:

We only need an AUXILIARY LINE !

Which should that be?                                           

Answer this in the next slide!

The best AUXILIARY LINE IS:

1. from B to AC
2. any perpendicular is good
3. from C to AB
4. from A to BC

Explanation:

You should not divide up side AC, which is 5 long.

Neither AB, because you have to calculate this side!

So the line goes from A to BC.

What is a good order now?
a. use sin 60 degrees to find AD
b. use sin angle B to find AB
c. calculate angle B

1. a, b, c
2. a, c, b
3. c, b, a
4. c, a, b

Explanation 33a:

(compare this to the exercise in the book)

A few points of attention:

+ Angle B can be calculated at first

+ before you calculate length AB, you need to know AD !

+ you need the SINE two times: to find AD and AB

Homework time ! (32 -36)