A skateboard ramp rises 3 m over a 4 m run, and its sloped surface is 5 m long. The ramp's outline is a right triangle.
The next lessons use a right triangle's sides constantly, so each side needs a name. Two of the names depend on which angle is marked.
Mark the angle at the bottom of the ramp, where the slope meets the ground.
The longest side, across from the right angle, is called the hypotenuse. Here it is the 5 m slope.
The side across from the marked angle is called its opposite side. The marked angle sits at the bottom, and across from it is the 3 m rise.
The side next to the marked angle is called its adjacent side. Here it is the 4 m run.
Now mark the other acute angle instead, at the top of the ramp. The triangle has not changed. Only the mark has moved. The hypotenuse stays the 5 m slope, because the right angle has not moved. But the opposite side has moved: it is now the 4 m run, across from the new marked angle. And the adjacent side is now the 3 m rise, next to the new marked angle.
One care point. Two sides touch the marked angle: the hypotenuse and the adjacent side. The adjacent side is the one that is not the longest. So 'next to the marked angle' means the non-hypotenuse side touching the marked angle.
A ladder leans against a wall. The ladder is 10 m long, its foot sits 6 m from the wall, and it touches the wall 8 m up. The angle is marked where the ladder meets the ground. Name each side.
Find the right angle:
the wall meets the ground at a right angle
Name the longest side:
across from the right angle is the 10 m ladder: the hypotenuse
Name the marked angle's opposite side:
across from the marked angle is the 8 m height up the wall
Name the marked angle's adjacent side:
next to the marked angle, and not the longest, is the 6 m stretch of ground
Hypotenuse: the 10 m ladder. Opposite side: the 8 m height. Adjacent side: the 6 m stretch of ground.
Now make the names automatic. Six triangles follow, and each asks the same question: which name fits the stated side?
A zip line: cable 13 m, vertical drop 5 m, ground run 12 m, the angle marked at the bottom. Which name fits the 5 m drop?
A kite string runs 25 m to a kite 20 m up, 15 m away over the ground. The angle is marked at the flier's hand. Which name fits the 25 m string?
A ramp rises 6 m over an 8 m run; its slope is 10 m. The angle is marked at the bottom. Which name fits the 8 m run?
A 3 m pole is steadied by a 5 m rope anchored 4 m from its base. The angle is marked at the pole's TOP. Which name fits the 4 m ground stretch?
A 6 m flagpole is held by a 10 m wire anchored 8 m from its base. The angle is marked at the pole's TOP. Which name fits the 6 m pole?
A 29 m support cable runs from the top of a 21 m tower to an anchor 20 m from its base. The angle is marked at the anchor. Which name fits the 29 m cable?
A loading ramp rises 1.2 m over a 1.6 m run; its slope is 2.0 m. The angle is marked at the bottom. Which pairing is correct?
In Alba's right triangle, the marked angle touches a 7 m side and a 25 m side (the longest); the third side is 24 m. Which side is the marked angle's adjacent side?
A right triangle has sides 2.1 m, 2.8 m and 3.5 m. With the angle marked at one corner, the 2.1 m side is its opposite side. The mark moves to the other acute corner. Which pairing is correct now?