MHB Length of sides of right triangle with 1 angle and 1 side

AI Thread Summary
The discussion revolves around determining the lengths of the sides of a right triangle given one angle and one side. The triangle in question is a 30-60-90 triangle with a height of 6, but the length of side BC is unspecified, leading to ambiguity in calculations. Participants note that without additional information, such as the relationship between other sides, it is impossible to definitively calculate the lengths. The original poster seeks guidance on whether this question fits within the trigonometry category. The conversation highlights the importance of having sufficient data to solve geometric problems accurately.
Dophs
Messages
1
Reaction score
0
Hello so I'm a high school student and I came up with this question and I wanted to know if this was possible to do?

View attachment 8044

So I tried to research and find a way to find the length of DC and I couldn't find anything, so I am here to ask for help, is this possible? I figured it would go in the trigonometry section, if not please tell me what sub-forum is belongs in.

So obviously I know the left, right triangle is a 30,60,90 and the height of the right, right triangle is 6 and obviously it has a 90 degree angle. I couldn't think of anyway to get any further due to the not drawn to scale part due to . BC could be 100, 4, 67, 21, so the angles would change of that triangle, but 6 is the height of both.
 

Attachments

  • Untitled.png
    Untitled.png
    9.5 KB · Views: 139
Mathematics news on Phys.org
Dophs said:
Hello so I'm a high school student and I came up with this question and I wanted to know if this was possible to do?
So I tried to research and find a way to find the length of DC and I couldn't find anything, so I am here to ask for help, is this possible? I figured it would go in the trigonometry section, if not please tell me what sub-forum is belongs in.

So obviously I know the left, right triangle is a 30,60,90 and the height of the right, right triangle is 6 and obviously it has a 90 degree angle. I couldn't think of anyway to get any further due to the not drawn to scale part due to . BC could be 100, 4, 67, 21, so the angles would change of that triangle, but 6 is the height of both.
You are right... BC can be any length we like unless we have more information, such as AD = AC.

-Dan
 
Thanks for reply and it is very informative.
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »
Thread 'Video on imaginary numbers and some queries'

Thread 'Video on imaginary numbers and some queries'

Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
View full post »
Thread 'Unit Circle Double Angle Derivations'

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
View full post »

Similar threads

MHB Find Length of Side in Right Triangle w/ 45°, 90°, and 45° Angle
Replies
2
Views
2K
B Understanding the Pythagorean Theorem
Replies
38
Views
4K
MHB Finding the Leg Lengths of a Right Triangle with an Acute Angle of 22°
Replies
2
Views
1K
MHB Difference of angles in a triangle
Replies
4
Views
2K
I Find Angles in Right Angle Triangles
Replies
4
Views
1K
MHB Acute angle of right triangles
Replies
4
Views
1K
B Find triangles with areas that are integers
Replies
20
Views
3K
MHB What is the Minimal Area of a Right-Angled Triangle with an Inradius of 1 Unit?
Replies
1
Views
1K
MHB What is the smallest side length BC of triangle ABC with fixed angle and area?
Replies
2
Views
1K
MHB Can You Find the Angle in This Isosceles Triangle Problem?
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top