You are here:

- Home
- Science
- Math for Kids
- Geometry
- Right Triangle

Advertisement

in a figure triangle PQR is right angled at R and S is the mid point of hypotenuse PQ. If RS = 25 cm and PR = 48 cm find QR.

When a right triangle is put in a circle, the hypotenuse is the diameter of the circle.

This means that the triangle PSR is symmetric and the triangle RSQ is symmetric since

PS, SQ, and SR are all radii of the circle.

Using the law of cosines, the measure of the angle opposite the side of length 48 can be found.

Using the law of cosines again and the fact that the angle on the other triangle is the supplement of the angle on this triangle, the far side of that triangle can be found.

Law of Cosines: a^2 + b^2 - 2ab*cosC = c^2.

Using this, cosC = (a^2 + b^2 - c^2)/(2ab).

From there, angel C can be found.

Once that is known, the angle in question is the supplement of that angle, so it is 180-A.

Once that is found, we have two sides that are both 25 and the angle between them,

and those can be used as a, b, and C in the Law of Cosine equation to find c^2.

Once this has been done, find the square root to get the answer. Note that since

it is a distance, we don't need to worry about the fact that square roots are both

positive and negative, for in this case, a negative value is not a distance.

I can answer whatever questions you ask except how to trisect an angle. The ones I can answer include constructing parallel lines, dividing a line into n sections, bisecting an angle, splitting an angle in half, and almost anything else that is done in geometry.

I have been assisting people in Geometry since the 80's.
**Education/Credentials**

I have an MS at Oregon State and a BS at Oregon State, both with honors.
**Awards and Honors**

I was the outstanding student in high school in the area of geometry and math in general.
**Past/Present Clients**

Over 8,500 people, mostly in math, with almost 450 in geometry.