Rectangular triangle

Mohssine

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Feb 20, 2021
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30
given a rectangular triangle ABC in A, B=38degree; D is a point of the line AC with CD=AC, proof that BD^2=7AC^2
 
Nice problem!
I can't wait to see what you have tried to see if you are trying to solve the problem the same way I would.
I am not sure if I have the correct diagram, so can we see your diagram?
Thanks!
 
Consider the triangle ABD:
BD2 = BA2 + (2AC)2

We are halfway there. What we have is BD in terms of BA and AC but we want BD purely in terms of AC. Now you just have to find a relationship between BA and AC and substitute.

Also, are you 100% sure B is 38 degrees? I have a feeling it should be 30 degrees.
 
Why not draw AD?
Great, you showed us the diagram! Now show us your attempt at solving this. This is a math help forum where we help students solve their problems and never do we solve problems for students.

You definitely can improve on your diagram by labeling some of the angles.
Try using the fact that you have two right triangles.
Please post back.
 
Now please show what work you have tried! We don't just do the work for you when you will learn more by exercising your own mind.

I took AB = c and calculated BD^2 and AC^2.
 
i just used phytagore i didnt solve the problem, do i have to use the angle 30? how though
 
Have you learnt trigonometry in class yet? This question requires a basic understanding of trigonometry...

I would recommend you to brush up and revise the 30-60 triangle and 45 triangle as they are the most common angles that will arise with the cleanest solutions :)
 
From google: "Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles"
This is what you have done, although maybe you have not been formally introduced to it.
The use of sin30 = 0.5 creates a relationship between the ratio of side lengths.

Once you formally learn trigonometry, the 45 triangle and 30 - 60 triangle will become useful as most algebraic trig problems cannot be done using the calculator:

1618369526084.png

The reason sin30 = 0.5 is because sinx = opposite side/hypotenuse = 1/2 = 0.5
These triangles can become a quick way to mentally arrive at the exact values of trig expressions involving angles of 30, 60, 45.
 
i will ask peterson to do it
First of its Dr Peterson, not peterson. 2nd of all I wish you good luck with having Dr Peterson solve your problem for you.
Again, this is a help forum not a homework service site. if you do not believe this, then read the posting guidelines.
 
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