Right Triangles and Trigonometry Exercises

Example 1

Find the value of x.

Hint

Mr. Pythagoras wouldn't let this triangle into his Pythagorean Triple Club even if it begged.

Example 2

Find the value of x.

Hint

In this triangle, x is the shortest leg.

Example 3

Find the value of x.

Hint

Both the legs of the triangle are the same length. That means that in terms of the Pythagorean Theorem, x = a = b.

Example 4

A triangle has side lengths of , , and . Is the triangle a right triangle?

Hint

What's the Converse Pythagorean Theorem again?

Example 5

Determine whether ∆XYZ is a right triangle and/or a Pythagorean triple if its vertices are at the points X (1, 1), Y (1, 7), and Z (9, 1).

Hint

A Pythagorean triple will always make a right triangle.

Example 6

If the distance between A and B is 26, what is the value of y?

Hint

Drawing a line from B down to the x-axis at a right angle might help.

Example 7

Find the value of x.

Hint

The Pythagorean Theorem can give us the hypotenuse of the largest triangle. Then, we can use the geometric mean to find a. Once we know a, we can figure out what x is.

Right Triangles and Trigonometry Exercises

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

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