12 min read

Introduction

Triangle measuring for real lengths and angles — ladders, roofs, and right-angled triangles.

How Long Is the Ladder?

A ladder rests against a wall. The foot is 1.5 m from the wall, and it meets the ground at 70 °. How long is the ladder? You cannot pace the sloping ladder easily — but trigonometry turns that angle and one known length into the missing side. Pythagoras handles the case when you know two sides and need the third in a right-angled triangle. Trigonometry means triangle measuring. That is all.

Example 1 — Picture the parts

For the angle at the ground: The wall height is opposite the angle. The ground distance is adjacent to the angle. The ladder is the hypotenuse (the longest side, opposite the right angle).

You will use Pythagoras, then sine, cosine and tangent to find missing sides and angles, including elevation and depression. Later lessons extend to the unit circle and graphs.

Practice

In a right-angled triangle, which side is always longest?

12 min read

Triangle measuring for real lengths and angles — ladders, roofs, and right-angled triangles.

A ladder rests against a wall. The foot is 1.5 m from the wall, and it meets the ground at 70 °. How long is the ladder? You cannot pace the sloping ladder easily — but trigonometry turns that angle and one known length into the missing side. Pythagoras handles the case when you know two sides and need the third in a right-angled triangle. Trigonometry means triangle measuring. That is all.

Example 1 — Picture the parts

For the angle at the ground: The wall height is opposite the angle. The ground distance is adjacent to the angle. The ladder is the hypotenuse (the longest side, opposite the right angle).

You will use Pythagoras, then sine, cosine and tangent to find missing sides and angles, including elevation and depression. Later lessons extend to the unit circle and graphs.

Practice

In a right-angled triangle, which side is always longest?