Pythagorean Theorem Word Problems

Pythagorean Theorem On Word Problems

Concept

Solve application problems that involve finding the side of a right triangle using the Pythagorean Theorem.

Rules

1. Substitute the given values in the Pythagorean Theorem.
$\fn_phv a^{2}+b^{2}=c^{2}$
2. Solve using order of operations.

Example

The fire escape ladder from one balcony to the next is 5 meters long. The bottom of the ladder is 2.7 meters to the right of the top of the ladder. What is the vertical distance between the balconies? Round your answer to the nearest tenth.

Solution

The length of the ladder is the hypotenuse, so 5 is substituted for c in the Pythagorean Theorem formula. 2.7 is one of the legs.
$\fn_phv a^{2}+b^{2}=c^{2}$
$\fn_phv 2.7^{2}+b^{2}=5^{2}$
$\fn_phv 7.29+b^{2}=25$
$\fn_phv b^{2}=25-7.29$
$\fn_phv b^{2}=17.71$
$\fn_phv b=\sqrt{17.71}\approx {\color{Red} 4.2}$
The vertical distance between the balconies is 4.2 meters.

Practice Pythagorean Theorem Word Problems

Practice Problem 1

If a right triangle has legs that measure 3 and 4, what is the length of the hypotenuse?

Practice Problem 2

Find the length of the missing side. Round the answer to the nearest tenth if necessary.

Practice Problem 3

To walk around the pond from point A to point B, you must walk 34 meters south and 41 meters east. If a bridge was build between points A and B across the pond, how many meters long would the bridge have to be? Round your answer to the nearest tenth.

Practice Problem 4

When decorating a cake, the frosting is put into a cone-shaped bag. If the bag has a radius of 7cm and a slant height of 25 cm, what is the actual height of the bag to the nearest tenth of a cm?

The hypotenuse is the side opposite of the right angle. It is the longest side.

The legs are the two sides that form the right angle.

Pythagorean theorem – the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.

Pre-requisite Skill
Pythagorean Theorem

Related Skill
Distance on a Coordinate Plane