In this lesson:
You will be able to:
Point to the right angle, the hypotenuse (opposite it), and the two legs. The hypotenuse is always the longest side.
Sides 15, 9, 12: the hypotenuse is 15. Write first.
where = hypotenuse, and = legs. For legs 3 and 4: .
Legs 6 and 8:
Legs 5 and 7:
74 has no square factor, so the answer stays (between 8 and 9).
When finding a leg, subtract:
Hypotenuse 13, leg 5:
Hypotenuse 10, leg 6:
A leg must be shorter than the hypotenuse.
Right-triangle legs 20 and 48. Find the hypotenuse.
Step 1: Find a common factor
Step 2: Recognize the triple: 5-12-13
Step 3: Scale back up:
Leg 6, hypotenuse 8 → , not 10.
Let be the longest side. Compare to :
Why: too short for a right angle → acute; too long → obtuse
Sides 7, 10, 12:
Sum bigger: longest side too short for a right angle, so acute.
Sides 5, 8, 11:
Sum smaller: longest side too long, so obtuse.
Which set of side lengths forms a right triangle?
(A) 9, 12, 16 (B) 10, 24, 26 (C) 6, 7, 10 (D) 8, 14, 17
Pause and check each one, then read on.
Answer: (B). , and 10-24-26 is 5-12-13 times 2.
Find the right triangle first. A TV screen is 36 in × 48 in. Find the diagonal.
Recognize: is → in
A 17-ft ladder leans on a wall, base 8 ft out. How high does it reach?
Find the right triangle: ladder = hypotenuse (17), ground = leg (8).
Recognize: 8-15-17 triple!
An isosceles triangle has sides 10, 10, and base 12. Find the height.
Half-base:
Height:
We stop at the height; using it for area comes in a later lesson.
Between two points, the horizontal and vertical gaps are the legs.
The distance between the points is the hypotenuse.
The lesson on the distance formula builds on exactly this idea.
Look for these signals:
Remember:
Watch out:
Up next: Special right triangles
Click to begin the narrated lesson
Pythagorean theorem