30-60-90 triangle example problem | Right triangles and trigonometry | Geometry | Khan Academy

TL;DR

Calculate the perimeter of triangle BED, which is located within a rectangle, given the length of one side and the trisected angles.

Transcript

So we have this rectangle right over here, and we're told that the length of AB is equal to 1. So that's labeled right over there. AB is equal to 1. And then they tell us that BE and BD trisect angle ABC. So BE and BD trisect angle ABC. So trisect means dividing it into 3 equal angles. So that means that this angle is equal to this angle is equal t... Read More

Key Insights

• 💁 The given information includes the length of one side of the rectangle and the trisected angles of a vertex within the rectangle.
• 🙃 Opposite sides of a rectangle are equal in length.
• 🔺 Trisecting an angle means dividing it into three equal angles.
• 🥳 30-60-90 triangles have side length ratios of 1:square root of 3:2.

Questions & Answers

Q: How can the perimeter of triangle BED be calculated within the rectangle?

The perimeter can be calculated by finding the lengths of the three sides within the triangle and adding them together.

Q: What does it mean for angle ABC to be trisected?

Trisecting angle ABC means dividing it into three equal angles, resulting in three angles of 30 degrees each.

Q: How can the lengths of the sides of the triangle be determined using 30-60-90 triangles?

The known side length of 1 can be used to calculate the other side lengths in the triangle using the ratios of 30-60-90 triangles.

Q: Why is it important to know that the figure is a rectangle?

Knowing that the figure is a rectangle allows us to determine that opposite sides are equal in length and all angles are 90 degrees, providing additional information for solving the problem.

Summary & Key Takeaways

• Given a rectangle with AB length equal to 1 and trisected angle ABC, determine the perimeter of triangle BED within the rectangle.

• By utilizing the properties of 30-60-90 triangles, the lengths of the sides can be calculated.

• The perimeter of triangle BED can be found by adding the lengths of the three sides and simplifying the expression.