In a Gandalf (45-45-90) triangle, both the legs equal each other.
Answer
Example 2
Find the values of x and y.
Hint
This is a Triforce (30-60-90) triangle, which means the hypotenuse is twice the length of the shortest leg.
Answer
Example 3
Find the values of x and y.
Hint
The hypotenuses of both the triangles equal each other.
Answer
Example 4
Find the perimeter of the figure.
Hint
The perimeter is the outermost edge. Each triangle is a different size, but they're both of the Gandalf variety. One side to find them all….
Answer
The perimeter is 3√2 + 6 + 3 + 3 ≈ 16.2.
Example 5
Find the value of x.
Hint
Every triangle is a Triforce (30-60-90) triangle. They get continuously smaller, with the long leg of the bigger triangle equaling the hypotenuse of the next size down.
Answer
Example 6
Find the perimeter of the largest triangle.
Hint
These are Triforce triangles, quite obviously. The height of the big triangle equals twice the height of the smaller triangles.
Answer
The perimeter is 30.
Example 7
What's the value of y in the figure below?
Hint
Think Triforce.
Answer
y = 32√3 ≈ 55.4
Example 8
∆ABC is a Gandalf (45-45-90) triangle with the 90° angle at A. Find the coordinates of A in quadrant I if given the following coordinates: B (-5, 1) and C (4, 10).
Hint
Using the distance formula, we can calculate the length of between B and C, which is the hypotenuse.
