TeXercises.com

Gleichschenklig rechtwinkliges Dreieck

About points...

We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.

That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.

About difficulty...

We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.

That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:

Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise

Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise

Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise

Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise

Level 5 -
Level 6 -

Exercise

https://texercises.com/exercise/gleichschenklig-rechtwinkliges-dreieck/

Question

Solution

Short

Video

\(\LaTeX\)

No explanation / solution video to this exercise has yet been created.

Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!

Exercise:
minipage.textwidth abc Betrachte das nebenstehe gleichschenklige rechtwinklige Dreieck mit der Basis b den Schenkeln a und dem Winkel alpha. abclist abc Bestimme die Höhe h des Dreiecks in Abhängigkeit von b. abc Bestimme die Länge a der Schenkel in Abhängigkeit von b. abc Bestimme sinalpha cosalpha und tanalpha ohne Taschenrechner und überprüfe deine Resultate mit der Tabelle im Theorieteil. abclist minipage hfill minipage.textwidth raggedleft GleichschenkligesRechtwinkligesDreieck. minipage

Solution:
abclist abc Der Winkel alpha muss gerade ^circ sein. Durch die Höhe h entstehen zwei neue gleichschenklige rechtwinklige Dreiecke. Somit ist die Höhe hfrac b. abc Mit dem Satz von Pythagoras bestimmen wir die Länge der Schenkel: a^ leftfrac bright^ + h^ leftfrac bright^ + leftfrac bright^ fracb^ &&|sqrt a fracbsqrt . abc Wir berechnen mit den Definitionen: sinalpha fracha fracfrac bfrac bsqrt fracsqrt cosalpha frac frac ba frac frac bfrac bsqrt fracsqrt tanalpha frachfrac b fracfrac bfrac b . Diese Resultate stimmen mit den Tabellenwerten überein. abclist

Meta Information

\(\LaTeX\)-Code

Contained in these collections:

Trigonometrie im rechtwinkligen Dreieck III by pw

6 | 7

Attributes & Decorations

Tags	anwendung, cosinus, geometrie, gleichschenkliges dreieck, mathematik, rechtwinkliges dreieck, sinus, tangens, trigonometrie, winkelfunktionen
Content image
Difficulty	(3, default)
Points	0 (default)
Language	(Deutsch)
Type	Calculative / Quantity
Creator	pw
Decoration
File
Link