### All ISEE Upper Level Math Resources

## Example Questions

### Example Question #1 : Right Triangles

A right triangle has a hypotenuse of 10 and a side of 6. What is the missing side?

**Possible Answers:**

**Correct answer:**

To find the missing side, use the Pythagorean Theorem . Plug in (remember c is always the hypotenuse!) so that . Simplify and you get Subtract 36 from both sides so that you get Take the square root of both sides. B is 8.

### Example Question #2 : Right Triangles

Refer to the above diagram. Which of the following quadratic equations would yield the value of as a solution?

**Possible Answers:**

**Correct answer:**

By the Pythagorean Theorem,

### Example Question #3 : Right Triangles

Note: Figure NOT drawn to scale.

Refer to the above diagram. Which of the following quadratic equations would yield the value of as a solution?

**Possible Answers:**

**Correct answer:**

By the Pythagorean Theorem,

### Example Question #4 : Right Triangles

Note: Figure NOT drawn to scale.

Refer to the above diagram.

Find the length of .

**Possible Answers:**

**Correct answer:**

First, find .

Since is an altitude of right to its hypotenuse,

by the Angle-Angle Postulate, so

### Example Question #5 : Right Triangles

Note: Figure NOT drawn to scale.

Refer to the above diagram.

Find the length of .

**Possible Answers:**

**Correct answer:**

First, find .

Since is an altitude of from its right angle to its hypotenuse,

by the Angle-Angle Postulate, so

### Example Question #6 : Right Triangles

Note: Figure NOT drawn to scale.

Refer to the above diagram. Evaluate .

**Possible Answers:**

**Correct answer:**

By the Pythagorean Theorem,

### Example Question #7 : Right Triangles

A right triangle with hypotenuse is inscribed in , a circle with radius 26. If , evaluate the length of .

**Possible Answers:**

Insufficient information is given to answer the question.

**Correct answer:**

The arcs intercepted by a right angle are both semicircles, so hypotenuse shares its endpoints with two semicircles. This makes a diameter of the circle, and .

By the Pythagorean Theorem,