Cayuga Heights 5th Grade Math Club
Problems for February 5, 2016
Right triangles and the Pythagorean Theorem
Right triangles have some special properties that can be very helpful when solving
math problems. A right triangle is a triangle with a single right angle. The side opposite
the right angle is called the hypotenuse and the other two sides are called the legs of the
triangle. The hypotenuse of a right triangle is always the longest side of the triangle,
because the angles opposite the legs of the triangle are always acute angles (smaller than
right angles).
The area of a right triangle is computed using the same formula as the area for any
triangle; one-half of the base of the triangle times its height. It’s particularly convenient
for right triangles because the two legs are the base and the height.
1. The sail of Charlotte’s boat is a right triangle that is 15 feet tall and 8 feet wide along
the bottom. What is the area of the sail?
2. When shining in the direction of a wall 12 feet away, Matthew’s movie projector illu-
minates a triangular region of the floor. If the illuminated region is 8 feet wide at the
widest point where it hits the wall, what is the area of the floor that is illuminated?
Remember that the angles of a triangle always add up to 180 degrees. Since a right
angle is 90 degrees, that means the other two angles add up to 90 degrees. They are said
to be complementary angles. For example, that means we can fit a right triangle together
with a copy of itself to make a rectangle.
3. Four copies of the same right triangle are glued together as shown. How big is the
blue angle in degrees?
