Drawing triangles given sides and angles

[Redinorun]

Hello, I would need some help with drawing these 3 triangles for my homework.
Would be nice if you could just help me to start drawing (what to do first) the right way. Thanks.

Homework Statement

a) Regular triangle:
b - a = 3cm
c = 6cm
γ = 120°

b) Regular triangle:
a + b + c = 16cm
α = 75°
β = 60°

c) Isosceles triangle:
a + h = 8cm
γ = 30°

Homework Equations

/

The Attempt at a Solution

a)

b)

c) I found out that on hand of that we know that α = β = 75°

 

[BvU]

I am afraid you will be needing some relevant equations to complete these triangles. Which ones could be useful here ?

 

[Redinorun]

We didn't use any equations at school. We just drew them. :(

 

[ehild]

Starting with a): Do you know the theorem that from any chord, the angles on the circumference are equal? See picture:

Given b-a, gamma and c. You can determine the angle delta. With delta, draw the yellow triangle, starting with the segment b-a. To c, draw the circle where the point C is positioned: c is the cord, from where the angle on the circumference is the given gamma.

 

[Redinorun]

Starting with a): Do you know the theorem that from any chord, the angles on the circumference are equal? See picture:

Given b-a, gamma and c. You can determine the angle delta. With delta, draw the yellow triangle, starting with the segment b-a. To c, draw the circle where the point C is positioned: c is the cord, from where the angle on the circumference is the given gamma.

View attachment 73839

Got that one. Basically after I saw your picture. I realized that both sides of your blue triangle are the same length (because b-a leaves you with a, right?) So I could calculate delta is 30, and on hand of that, that the pink marked corner is 150. That makes it fairly easy to draw the triangle. Thank you. :)

 

[ehild]

Got that one. Basically after I saw your picture. I realized that both sides of your blue triangle are the same length (because b-a leaves you with a, right?) So I could calculate delta is 30, and on hand of that, that the pink marked corner is 150. That makes it fairly easy to draw the triangle. Thank you. :)

It is right, and you do not even need the circle...What about b) can you draw it?

ehild

 

[ehild]

A little help to b) See picture.

 

[Redinorun]

A little help to b) See picture.

View attachment 73844

I actually made it. Thanks! Your pictures actually really help. The blue corner is 37,5 and the pink one is 30. At the top when the lines meet at C you just draw the same corners again, but down (because again, we have a, a and b, b) and that's it! Thanks!

 

[ehild]

I actually made it. Thanks! Your pictures actually really help. The blue corner is 37,5 and the pink one is 30. At the top when the lines meet at C you just draw the same corners again, but down (because again, we have a, a and b, b) and that's it! Thanks!

Good! What about the third triangle? I do not understand the problem text. Is a the base or one of the equal sides? Does h belong to a or to the other side? Which angle is given?

ehild

 

[Redinorun]

Good! What about the third triangle? I do not understand the problem text. Is a the base or one of the equal sides? Does h belong to a or to the other side? Which angle is given?

ehild

"a" is one of the equal sides (just like usual). (c is the base) "h" is the height of the triangle. The angle gamma (by the point C) is given 30. So the thing also given is one of the equal sides + the height (a + h).

 

[Redinorun]

A picture of the problem.

 

[ehild]

This is very similar to the second one. You can draw the big right triangle...

 

[Redinorun]

This is very similar to the second one. You can draw the big right triangle...

View attachment 73847

Oh, how did I not see that?! But wait... ugh... I can't figure out the angles on this one. Nor the length of a.

 

[ehild]

The leg of the right triangle is a+h. The blue angle on it is 90°, and you can determine the pink one from gamma. gamma/2 is the exterior angle of the yellow isosceles triangle.

 

[Redinorun]

The leg of the right triangle is a+h. The blue angle on it is 90°, and you can determine the pink one from gamma. gamma/2 is the exterior angle of the yellow isosceles triangle.

Oh, right, right right! I got stuck on the pink one, for some reason I couldn't figure out that I had to gamma/2, to get the top of the yellow one. Got it now. It's very "slim".
Now I know, always look for isosceles triangles and similar.

Thanks again for taking the time to help me. :)

 

[ehild]

You are welcome. :)