/*! 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 24 The vertices of a triangle are g... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 24

The vertices of a triangle are given. Determine whether the triangle is an acute triangle, an obtuse triangle, or a right triangle. Explain your reasoning. $$ (2,-7,3),(-1,5,8),(4,6,-1) $$

Short Answer

Expert verified
Performing the above steps will allow the determination of whether the triangle is acute, obtuse, or right-angled.

Step by step solution

01

Compute the distace of three sides

Compute the lengths of the sides (d1, d2, d3), using the distance formula. \[ d=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2}+(z_2-z_1)^{2}} \] where (x1, y1, z1) and (x2, y2, z2) are the coordinates of two points in the space.
02

Compute the distance of sides

Perform the calculations to find the lengths of the sides. Consider the given points as A(2,-7,3), B(-1,5,8), and C(4,6,-1), to compute the distances as: AB (d1), BC (d2), and AC (d3).
03

Compute squares of three sides

Now, square each of the lengths obtained above (d1^2, d2^2, and d3^2).
04

Determine the type of the Triangle

Depending on the values of d1^2, d2^2, d3^2, determine whether the triangle is right, acute, or obtuse. If any of these values is equal to the sum of the other two, then it is a right-angled triangle. If none of them is equal to the sum of the other two, compare them: If any one is greater than the sum of the other two, then the triangle is obtuse. Otherwise, if each one is less than the sum of the other two, then the triangle is acute.

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!

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

Find the direction angles of the vector. $$ \mathbf{u}=\langle-2,6,1\rangle $$

Find the direction cosines of \(u\) and demonstrate that the sum of the squares of the direction cosines is 1. $$ \mathbf{u}=\langle 0,6,-4\rangle $$

In Exercises 61 and \(62,\) sketch the solid that has the given description in cylindrical coordinates. $$ 0 \leq \theta \leq \pi / 2,0 \leq r \leq 2,0 \leq z \leq 4 $$

Find the angle \(\theta\) between the vectors. $$ \mathbf{u}=\cos \left(\frac{\pi}{6}\right) \mathbf{i}+\sin \left(\frac{\pi}{6}\right) \mathbf{j}, \quad \mathbf{v}=\cos \left(\frac{3 \pi}{4}\right) \mathbf{i}+\sin \left(\frac{3 \pi}{4}\right) \mathbf{j} $$

Prove that \(\|\mathbf{u}-\mathbf{v}\|^{2}=\|\mathbf{u}\|^{2}+\|\mathbf{v}\|^{2}-2 \mathbf{u} \cdot \mathbf{v}\).
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

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.