Mates y TIC - Maths and ICT

Actividades de Matemáticas con TIC - Math Activities with ICT - - - ( Ricardo García Mesa

Archive for January, 2018

Trigonometría y repaso

Posted by ricardogm on 28th January 2018

Muy buenas

1. Hoy empezaremos creando una versión simplificada de este applet:

Para ello aprovecharemos los ejes, dibujando la circunferencia con centro en (0,0) y dándole radio 1. Prestad atención y enviadme el resultado.

2. Ahora comenzamos el repaso, primero con unos ejercicios de Gauss, que corregiremos con Symbolab.




3. Y ahora un par de problemas:

a) Un hotel adquirió un total de 200 unidades entre almohadas, mantas y edredones, gastando un total de 7500 euros. El precio de una almohada es de 16 euros, el de una manta es de 50 euros y el de un edredón es de 80 euros. Además, el número de almohadas compradas es igual al número de mantas más el número de edredones. ¿Cuántas almohadas, mantas y edredones ha comprado el hotel?

b) Una empresa desea disponer de dinero en efectivo en euros, dólares y libras esterlinas. El valor total entre las tres monedas da de ser igual a 264000 euros. Se quiere que el valor del dinero disponible en euros sea el doble del valor del dinero en dólares, y que el valor del dinero en libras sea la décima parte del dinero en euros.

Si se supone que una libra esterlina es igual a 1,5 euros y un dólar es igual a 1,1 euros, se pide determinar la cantidad de euros, dólares y libras esterlinas que la empresa ha de tener disponible.

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Trigonometry 2

Posted by ricardogm on 25th January 2018


We have some things to do:

1. Solve these problems in your notebook while I try to correct your clinometers. Make drawings, of course.

1The known data for a right triangle ABC is a = 5 m and B = 41.7°. Solve the triangle.

2 The known data for a right triangle ABC is b = 3 m and B = 54.6°. Solve the triangle.

3 The known data for a right triangle ABC is a = 6 m and b = 4 m. Solve the triangle.

4 The known data for a right triangle ABC is b = 3 m and c = 5 m. Solve the triangle.

5 A tree 50 m tall casts a shadow 60 m long. Find the angle of elevation of the sun at that time.

6 An airship is flying at an altitude of 800 m when it spots a village in the distance with a depression angle of 12°. How far is the village from where the plane is flying over?

7Find the radius of a circle knowing that a chord of 24.6 m has a corresponding arc of 70°.

8 Calculate the area of a triangular field, knowing that two of its sides measure 80 m and 130 m and between them is an angle of 70°.

9Calculate the height of a tree, knowing that from a point on the ground the top of the tree can be seen at an angle of 30º and from 10 m closer the top can be seen at an angle of 60°.

10 The length of the side of a regular octagon is 12 m. Find the radii of the inscribed and circumscribed circles.

11 Calculate the length of the side and the apothem of a regular octagon inscribed in a circle with a radius of 49 centimeters.

12Three towns A, B and C are connected by roads which form a triangle. The distance from A to C is 6 km and from B to C, 9 km. The angle between these roads is 120°. How far are the towns A and B from each other?

UPDATE: here you have the solutions.

2. More problems.

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Sistemas de inecuaciones con dos incógnitas

Posted by ricardogm on 21st January 2018

Muy buenas

Hoy resolveremos gráficamente sistemas de inecuaciones con dos incógnitas, en la libreta. Usaremos el geogebra para corregir. Presten atención.



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Trigonometry 1

Posted by ricardogm on 18th January 2018


We are starting with the awesome world of trigonometry.

1. Project: clinometer


The picture above shows you the materials you’ll need to create a very simple clinometer (that is, a device to measure degrees of inclination, or slope). There are other designs, maybe better, but that’s mine, and it’s pretty cheap. In fact, other than the wooden lath, the rest of the materials should be in your school bag, or at home. This particular example is a bit ugly, I hope yours to be much nicer.


1. You’ll need to make a little hole in the right place of the protractor (the center of the circle, it’s usually marked clearly). You can use sophisticated machines, but a hot needle is probably the easier way. Just be careful. Don’t use a nuclear weapon, please.

2. Draw a line in the wooden lath, parallel to the side. The lath, of course, should be perfectly straight. Mine is a bit swill

3. Fix the nut (or another weight) to exactly 90º. You can use a reversible solution to not ruin your protractor (adhesive tape, for instance)

4. Nail down the protractor to the lath, in the middle of it and on the line you just draw.

5. Put your name on the device. I suggest using the wooden part, it’s easier.

6. At this point, it’s time to free your artistic part of the brain. Decorate the thing with something fun, or significant for you. Paint it, for example, write a song, draw a scary tatoo… It’s up to you.

Deadline: friday 26th. No excuses allowed. Examples of popular excuses: my dog ate it, my brother ate it, I ate my dog, etc.

NOTE: one clinometer per each one of you.

The following week (if the weather is nice enough) we are going to measure the height of different things with this humble device and your amazing trigonometry knowledge: trees, a hill, this school..

2. Trigonometric ratios:

We are going to create a similar applet to this one. Send it to my mail, as usual.

3. What does SOH-CAH-TOA mean? Find it out and send me the answer.

4. Using a protractor.

5. Degrees and radians.

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Posted by ricardogm on 11th January 2018


Today we are going to work with Geogebra. Pay attention to the teacher, take notes and send me the files you create.

1. A simple one to make Homer bigger or smaller. You can download this image:

2. This one creates similar polygons.


3. And another one with much more detail, showing lenghts and areas. Pay attention


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