Calculating Triangle Side Length with Known Angles and Radius

In summary, the formula for finding the length of a triangle's side depends on the type of triangle. You can use the Pythagorean theorem for a right triangle, divide the perimeter by 3 for an equilateral triangle, and use the law of cosines or law of sines for a scalene or isosceles triangle. You need at least one side length to find the length of a triangle's side, and knowing all three angles does not provide enough information. To find the length of a triangle's side, you need to know the length of at least two other sides or one side and an opposite angle. The length of a triangle's side cannot be negative, and it is typically measured using the same units as the
  • #1
BrentK
21
0
Hi there.
Can someone tell me how to calculate the length of "a", shown in these drawings?
"r" is the radius of the corner, so these 2 sides have the same length.
"C" is 90 deg
angle "B" is known (the angle of the corner)

Here are the diagrams. First example 45 degree corner, second example 75 deg corner.

Many thanks in advance for your help! (Nerd) ;)

View attachment 8683

View attachment 8684
 

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  • #2
If I understand the problem correctly, the answer is $a = r\tan\bigl(\frac12B\bigr)$.
 
  • #3
Thanks Opalg!
That works perfectly!
So easy... I was trying to hard (Dull)
 

FAQ: Calculating Triangle Side Length with Known Angles and Radius

1. What is the formula for finding the length of a triangle's side?

The formula for finding the length of a triangle's side depends on the type of triangle. For a right triangle, you can use the Pythagorean theorem (a² + b² = c²) to find the length of the hypotenuse. For an equilateral triangle, all three sides are equal, so you can divide the perimeter by 3 to find the length of each side. For a scalene or isosceles triangle, you can use the law of cosines or the law of sines to find the length of a side.

2. Can I find the length of a triangle's side if I only know the angles?

No, you need at least one side length to find the length of a triangle's side. If you know all three angles of a triangle, you can use the law of sines or the law of cosines to find the length of a side, but you would still need to know the length of at least one other side.

3. How many sides of a triangle do I need to know to find the length of the remaining side?

To find the length of a triangle's side, you need to know the length of at least two other sides or the length of one side and an angle opposite to it. If you know all three sides, you can use the law of cosines to find the length of the remaining side. If you know two sides and the angle between them, you can use the law of sines to find the length of the remaining side.

4. Can the length of a triangle's side be negative?

No, the length of a triangle's side cannot be negative. Length is a physical measurement and cannot have a negative value. If you get a negative answer when solving for the length of a triangle's side, it means that there was an error in your calculations.

5. What units are used to measure the length of a triangle's side?

The length of a triangle's side is typically measured using the same units as the other sides and angles of the triangle. Common units include centimeters, inches, and degrees. It is important to use consistent units when solving for the length of a triangle's side.

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