/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 12 Construct a right triangle with ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 12

Construct a right triangle with legs about 2 inches and 3 inches in length, respectively.

Short Answer

Expert verified
Draw lines 2 inches and 3 inches long, perpendicular to each other.

Step by step solution

01

- Draw the First Leg

Use a ruler to draw a straight line that is 2 inches long. Label the endpoints of this line as point A and point B.
02

- Draw the Second Leg

From point B, draw another straight line that is 3 inches long and perpendicular to the first leg. Label the endpoint of this line as point C.
03

- Complete the Triangle

Draw a line connecting point A to point C. This line is the hypotenuse of the right triangle.
04

- Verify the Right Angle

Use a protractor to ensure the angle at point B is 90 degrees, confirming it is a right triangle.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

geometric construction
Geometric construction involves creating shapes, angles, and lines accurately using simple tools like a ruler and a protractor. Constructing a right triangle starts with drawing the first leg of the triangle. This requires a perfectly straight line, which means using a ruler is essential. For the given exercise, start by drawing a 2-inch line. Label its endpoints as A and B. Next, you draw another line, perpendicular to the first, and 3 inches long from point B. This line's endpoint should be labeled as C. Using this method ensures precise and clear construction of the triangle.
triangle properties
Triangles have several important properties, especially right triangles. A right triangle has one angle that is exactly 90 degrees, known as the right angle. The lengths of the sides of a triangle are crucial too. For right triangles, the sides that form the right angle are called the legs, and the longest side opposite the right angle is called the hypotenuse. In our exercise, the legs have lengths of 2 inches and 3 inches. Knowing these properties helps us understand the relationship between the sides and angles in a right triangle.
right angle verification
To ensure you have constructed a right triangle correctly, verifying the right angle is crucial. After drawing your triangle, use a protractor to measure the angle at point B. It should be exactly 90 degrees. If it is not, adjust accordingly. This step is vital as it confirms the triangle is indeed a right triangle, meaning it has one angle precisely at 90 degrees. Verification also helps in solidifying our understanding of geometric accuracy and construction.
hypotenuse
The hypotenuse is the longest side in a right triangle, found opposite the right angle. Once you have drawn the two legs and verified the right angle, the line connecting points A and C is the hypotenuse. It's important to note that according to the Pythagorean theorem, the length of the hypotenuse can be calculated using the formula \(\text{AC} = \sqrt{\text{AB}^2 + \text{BC}^2}\), where AB and BC are the lengths of the legs. For our triangle with legs of 2 inches and 3 inches, the hypotenuse would be \(\text{AC} = \sqrt{2^2 + 3^2} = \sqrt{13}\) inches. Understanding the hypotenuse helps in a wide range of geometric and trigonometric applications.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

To measure the distance across a canyon, Diana stood at the edge of the canyon at point \(P\) and sighted a point \(Q\) on the far rim. Without raising or lowering her eyes, she turned around and sighted a point \(S\) on the ground. She then measured the distance between \(P\) and \(S\) and found it to be \(45 \mathrm{ft}\). She concluded that the width of the canyon is also \(45 \mathrm{ft}\). Why is this true?

Every triangle has three altitudes, angle bisectors, and medians. Describe the differences among these line segments.

Draw a segment about 2 inches long and a second segment 5 inches long. Construct an isosceles triangle with the base as the 2 -inch segment and each side as the 5 -inch segment.

Draw a scalene acute triangle and construct its three medians. Label the centroid.

Draw a scalene obtuse triangle and construct its three altitudes. Label the orthocenter.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.