All ISEE Upper Level Math Resources
Example Questions
Example Question #45 : Geometry
A right triangle has a hypotenuse of 10 and a side of 6. What is the missing side?
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 #1 : Triangles
Refer to the above diagram. Which of the following quadratic equations would yield the value of as a solution?
By the Pythagorean Theorem,
Example Question #1 : 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?
By the Pythagorean Theorem,
Example Question #2 : Triangles
Note: Figure NOT drawn to scale.
Refer to the above diagram.
Find the length of .
First, find .
Since is an altitude of right
to its hypotenuse,
by the Angle-Angle Postulate, so
Example Question #2 : Triangles
Note: Figure NOT drawn to scale.
Refer to the above diagram.
Find the length of .
First, find .
Since is an altitude of
from its right angle to its hypotenuse,
by the Angle-Angle Postulate, so
Example Question #3 : Triangles
Note: Figure NOT drawn to scale.
Refer to the above diagram. Evaluate .
By the Pythagorean Theorem,
Example Question #3 : Triangles
A right triangle with hypotenuse
is inscribed in
, a circle with radius 26. If
, evaluate the length of
.
Insufficient information is given to answer the question.
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,
All ISEE Upper Level Math Resources
