6. 2D Geometry

Remember that when working with the Pythagorean theorem, we must be working with a right triangle.

Remember the Pythagorean theorem is:

\displaystyle a^2+b^2=c^2

\bm{a, b}

lengths of legs of the right triangle

\bm{c}

length of the hypotenuse

To apply the Pythagorean theorem to real-life situations:

Look for right triangles

Choose which side, hypotenuse or a shorter side, you are trying to find

Substitute the known side lengths in to the Pythagorean theorem

Solve for the unknown length

The Pythagorean theorem can be applied to many contextual situations, including but not limited to: archirecture, construction, sailing, and space flight.

Consider a cone with slant height 13\, \text{m} and perpendicular height 5\, \text{m}.

a

Find the length of the radius, r, of the base of this cone.

Worked Solution

b

Find the length of the diameter of the cone's base.

Worked Solution

The screen on a handheld device has dimensions 8 \text{ cm} by 4 \text{ cm}, and a diagonal of length x \text{ cm}.

Find the value of x, correct to two decimal places.

Worked Solution

A ladder is leaning against a wall. The base of the ladder is 6 feet away from the wall, and the ladder is 7 feet long. How far up the wall does the ladder reach? Round your answer to two decimal places.

Worked Solution

Idea summary

To apply the Pythagorean theorem to real-life situations:

Look for right triangles

Choose which side, hypotenuse or a shorter side, you are trying to find

Substitute the known side lengths in to the Pythagorean theorem

Solve for the unknown length