The triangles here are the special ones, so the angles come out exactly rather than as a rounded decimal. The area questions use two sides and the angle between them.
A right triangle has legs 5 and 5. Find the acute angles
The legs are equal, so the triangle is isosceles.
The two acute angles share the remaining 90 degrees.
The answer is 45∘ and 45∘.
Where students go wrong
Using the area formula with an angle that is not between the two sides. Half a b sin C only works when C sits between a and b; with any other angle it gives a number that means nothing.
Also called finding missing angles, trigonometry and area or inverse trig ratios.
Questions about these worksheets
Yes. Every solving right triangles sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the solving right triangles questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
Using the area formula with an angle that is not between the two sides. Half a b sin C only works when C sits between a and b; with any other angle it gives a number that means nothing.