Question
The measure of one of the small angles of a right triangle is 45 less than twice the measure of the other small angle. Find the
measure of both angles.
Provide your answer below:

Let’s call the measure of the smaller angle . According to the problem, the other small angle will then be . Since we know that the sum of the two smaller angles in a right triangle equals 90 degrees (because one angle is 90 degrees), we can set up the equation:

Simplifying this gives:

Adding 45 to both sides:

Dividing by 3:

Now, substituting back to find the other angle:

So, both angles are degrees.

Now, let’s dig into a bit more about right triangles and angles! Did you know that the unique combination of angles in a right triangle – especially the triangle – creates an isosceles triangle where the legs are equal in length? This type of triangle is not only neat geometrically, but it’s also a fundamental shape that comes up frequently in various fields, including architecture and engineering!

On a practical note, a triangle has sides in the ratio of . This means if you know the length of one leg, you can easily find the hypotenuse by multiplying the leg length by . This little property is a real time-saver on a construction site when you need to calculate lengths quickly without a calculator!