Andre is building a structure out of playing cards. Each card is 6.3 cm long.

Question

He tries leaning the cards against each other so that the angle at the top is 90 degrees. Find the distance between the edges of the cards to the nearest tenth.

Answer 1

A² + B² = C²

 

6.3²+ 6.3²=C²

 

C²= 79.38

 

C=8.9

Answer 2

HI Kayla, if the angle at the top is 90 degrees, and each card is 6.3 cm long, this means the cards form an isosceles triangle. The base angles of the triangle will be 45 degrees.

 

If we drop a vertical line from the apex, or 90 degree angle, it will split the 90 degree angle into two 45 degree angles and split the base of the original triangle into two equal parts.

 

This gives us a 45 degree right triangle, which has the relationship of 1, 1, and the √2, where √2 represents the hypotenuse of the triangle.

 

Let x represent the length of the leg of the triangle with the hypotenuse of 6.3.

 

We can set up the proportion:

 

1 / √2 :: x / 6.3 

 

Solve for x:

 

x = 6.3 / √2, or about 4.45 cm

 

Since we split the base of the original isosceles triangle when we dropped the vertical line, the full base will be 2x, or 8.9 cm.

 

The two cards with an angle of 90 degrees at the apex will have their edges about 8.9 cm apart.

 

Questions?