Special Right Triangles: 30-60-90

Special Right Triangles:

​30^o-60^o-90^o Triangles

Learning Targets

CO: I will solve missing side lengths by applying relationships in special right triangle 30-60-90.

LO: I will compare angle relationships and solve for the relationship in side lengths in a 30-60-90 triangle.

EQ: How can I use proportions to find missing side lengths in special right triangles?

Open Ended

Go to: https://www.geogebra.org/m/qkCm364m

Create a triangle by moving points A or B to stretch or compress the given triangle.

Use the snipping tool to take a picture of your triangle.

Open Ended

Staying on https://www.geogebra.org/m/qkCm364m

Record the following based on your triangle:

The angle measures of the triangle:

$$\angle B\ =\ ,\ \angle C=\ ,\ \angle A=$$

The lengths of the sides of the triangles

$$AB=,\ BC=,\ AC=$$

Draw

Looking at the triangle you created on: https://www.geogebra.org/m/qkCm364m

Draw the triangle. Label the sides of your triangle as hypotenuse, shorter leg, and longer leg.

Open Ended

Using the triangle from: https://www.geogebra.org/m/qkCm364m

Perform the following calculations:

$$\frac{hypotenuse}{2}=$$

$$\frac{longer\ leg}{\sqrt[]{3}}=$$

Open Ended

Go to: https://www.geogebra.org/m/qkCm364m

With a partner at your table group, look over each other's data and calculations. What do you notice about the triangle?

​Now let's explore it another way. Let's start with an equilateral triangle with interior angles all being 60^o and side lengths of 2.

Fill in the Blank

If you draw a perpendicular bisector on an equilateral triangle, what are the measures of the angles of the 2 triangles created, $$\angle C\ ,\ \angle DAC\ ,\ and\ \angle ADC$$ ?

,

,

&

Fill in the Blank

What would the ratio between the short leg and the hypotenuse be? (Think about the side lengths of an equilateral triangle?)

Write your answer in the following format:

short leg length : hypotenuse length

:

Math Response

Using the Pythagorean Theorem, what would the length of the long side be if the length of the short side was 1 unit, and the length of the hypotenuse is 2 units?

Put your answer in simplified radical form.

Type answer here

Correct Answer: \sqrt{3}

Deg^°

Rad

Multiple Choice

True or False: All 30-60-90 triangles are similar.

• True

• False

True!

Quick Calculations

​Now, try a practice problem.

Fill in the Blank

If the long leg of a 30-60-90 triangle is

$$5\sqrt{3}$$  , what is the length of the hypotenuse?

Open Ended

After going through this lesson, which type of problem(s) do you feel like you can do well? Explain.

Open Ended

After going through this lesson, which type of problem(s) do you feel like you are still struggling with? Explain.