Whether you are estimating on the spot or checking a result somebody else gave you, the triangle scale factor calculator is the quickest way to get from ab (a), ∠bac (α₁), ∠edf (α₂), bc (b), ∠abc (β₁), ∠def (β₂), ac (c), ∠acb (γ₁), ∠dfe (γ₂) and scale factor (k) to semi- perimeter of △def, semi-perimeter of △abc and perimeter of △abc.
What Is the Triangle Scale Factor Calculator?
The triangle scale factor calculator works through ab (a), ∠bac (α₁), ∠edf (α₂), bc (b), ∠abc (β₁), ∠def (β₂), ac (c), ∠acb (γ₁), ∠dfe (γ₂) and scale factor (k) to give you semi- perimeter of △def, semi-perimeter of △abc and perimeter of △abc.
It is aimed at the case where you know the method but not the arithmetic: schoolwork, a quick check on a worked example, or a figure that needs to be right first time.
How the Triangle Scale Factor Works
Each step is applied in order and depends only on the values before it, which makes it possible to follow the calculation rather than take it on trust.
If you are working through the same problem by hand afterwards, compare the intermediate values. That is where a mistake usually shows itself.
Checking Your Own Working
Round sensibly as you go and keep the full precision in the calculator. Rounding too early is the most common way of getting a right method to give a wrong answer.
Where a result should be a whole number, such as a count, check it against the constraint that produced it. A fraction of a person is a sign that something upstream needs revisiting.
A Worked Example
Working through an example, with ab (a) set to 10, ∠bac (α₁) set to 5, ∠edf (α₂) set to 2, the calculator returns semi-perimeter of △abc of 56, and semi- perimeter of △def of 280, and t1 of 46. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out semi- perimeter of △def?
Enter ab (a), ∠bac (α₁), ∠edf (α₂), bc (b), ∠abc (β₁), ∠def (β₂), ac (c), ∠acb (γ₁), ∠dfe (γ₂) and scale factor (k). The calculator then works through the relationship and reports semi- perimeter of △def, semi-perimeter of △abc and perimeter of △abc.
What does the triangle scale factor actually calculate?
It takes ab (a), ∠bac (α₁), ∠edf (α₂), bc (b), ∠abc (β₁), ∠def (β₂), ac (c), ∠acb (γ₁), ∠dfe (γ₂) and scale factor (k) and converts them into semi- perimeter of △def, semi-perimeter of △abc and perimeter of △abc using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter ab (a)?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Do I have to fill in every field?
Only the fields a particular result depends on. If you leave one blank, the results that need it simply show a note instead of a number, and everything else still works.
Why does a small change in one value move the answer so much?
That happens when an output depends on a ratio, because dividing by a small number magnifies any change in it. Check the units first, then check whether the value you entered is in the range the relationship was designed for.