- Identify and use the ratios involved with 30∘−60∘−90∘ triangles.
- Identify and use ratios involved with equilateral triangles.
Equilateral triangles are also ___________________.
Notice what happens when you divide an equilateral triangle in half:
- An altitude is a line that is ______________________________ to the base of a triangle.
- The hypotenuse of the resulting triangle is the side of the original, and the shorter leg is half of an original side.
- The altitude makes a 90∘ angle at the base and splits the 60∘ angle into two __________ angles.
The ________________ is the longest side of any right triangle.
Just as you found a constant ratio between the sides of an isosceles right triangle, you can find constant ratios here as well. Use the Pythagorean Theorem to discover these important relationships.
Find the length of the missing leg in the following triangle. Use the Pythagorean Theorem to find your answer.
In this diagram, you are given two measurements:
- The hypotenuse (which is side ___________ ) is 2 cm and
- The shorter leg (which is side ___________ ) is 1 cm
We can try this again using a hypotenuse of 6 feet.
The special relationship is as follows:
- the hypotenuse will always be twice the length of the shorter leg,
- and the longer leg is always the product of the length of the shorter leg and 3√.
In ratio form, the sides, in order from shortest to longest are in the extended ratio
What is the length of the missing leg in the triangle below?
The special relationship is:
- the hypotenuse is _____________________ the length of the shorter leg, and
- the longer leg is the _______________________ of the length of the shorter leg and 3√
First, you know that the hypotenuse is 16 because it is across from the right angle.
Therefore, the other 2 sides are the legs in this triangle.
What is AC below?
________ : ________ : ________
The diagram below shows the shadow a flagpole casts at a certain time of day.
If the length of the shadow cast by the flagpole is 13m, what is the height of the flagpole and what is the length of the hypotenuse of the right triangle shown?
The height of the flagpole is the longer leg in the triangle, so use the special right triangle ratios (along with the given height of the base of the triangle) to find the length of the missing sides, the flagpole height and the hypotenuse.
What is the length of the altitude in the triangle below?
Graphic Organizer for Lessons 9 and 10