FST
Right Triangles and Trig
Investigation: Right Triangle Ratios
Name: ________________________________
Date: _________________________________
Essential Question: How can you find a leg of a right triangle when you know the other leg and one acute
angle?
Step 1: In the figure to the right you will find a 40 degree angle. A point has been marked every 2
centimeters on a side as shown. Perpendicular segments have been drawn through the 3 points.
Step2: Measure the legs of each right triangle. Copy and complete the table.
Triangle
Adjacent
Leg
ΔABC
2 cm
ΔADE
4 cm
ΔAFG
6 cm
Opposite
Leg
𝑶𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝑳𝒆𝒈
𝑨𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝑳𝒆𝒈
𝐵𝐶
𝐴𝐶
𝐵𝐶
Step 3: Substitute the values you found into the proportions 𝐷𝐸 = 𝐴𝐸 and 𝐴𝐶 =
values equal? Explain what that means about the triangles.
𝐷𝐸
𝐴𝐸
. Cross multiply, do the
Step 4: Connection: Make a conjecture, about the ratio of the lengths of the legs in a right triangle. Connect
the relationship you found in the table and what you concluded about your triangles.
Step 5: Test your conjecture by making your own diagram. Draw a different size angle and 3 points on one
of the sides 3 cm apart. (Show your test!)
Triangle
Adjacent
Leg
ΔABC
3 cm
ΔADE
6 cm
ΔAFG
9 cm
Opposite
Leg
𝑶𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝑳𝒆𝒈
𝑨𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝑳𝒆𝒈