Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Problem 5

In questions 1-11 \(\Delta \mathrm{ABC}\) has a right angle at \(\mathrm{C}\). Calculate AC given \(\mathrm{AB}=15 \mathrm{~cm}\) and \(\mathrm{BC}=12 \mathrm{~cm}\)

Short Answer

Expert verified
Answer: 9 cm

Step by step solution

01

Write down the Pythagorean theorem formula

In a right-angled triangle, the Pythagorean theorem states that: \(AB^2 = AC^2 + BC^2\)
02

Identify the known values and the unknown value in the equation

We are given the lengths of sides AB (15 cm) and BC (12 cm), and we need to find the length of side AC. \(15^2 = AC^2 + 12^2\)
03

Substitute the known values into the equation and solve for the unknown value (AC^2)

Replace AB with 15 and BC with 12: \(15^2 = AC^2 + 12^2\) \(225 = AC^2 + 144\)
04

Solve for AC^2

Subtract 144 from both sides of the equation: \(225 - 144 = AC^2\) \(81 = AC^2\)
05

Find the square root of AC^2 to get the length of side AC

Take the square root of both sides of the equation: \(\sqrt{81} = \sqrt{AC^2}\) \(9 = AC\) The length of side AC is 9 cm.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

In questions 16-23 solve \(\Delta \mathrm{XYZ}\) given \(\mathrm{XZ}=85 \mathrm{~cm}, \mathrm{YZ}=70 \mathrm{~cm}\) and \(Z=59^{\circ}\).

Find the resultant of the forces shown in Figure \(5.14\). a. b.

In questions 1-11 \(\Delta \mathrm{ABC}\) has a right angle at \(\mathrm{C}\). Calculate \(\sin A\) given \(\mathrm{AC}=10 \mathrm{~cm}\) and \(\mathrm{AB}=14 \mathrm{~cm}\)

A tower has a bearing of \(37^{\circ} 00^{\prime}\) when measured from a point \(\mathrm{O}\), and is \(973 \mathrm{~m}\) distant from \(\mathrm{O}\). A chimney has a bearing of \(100^{\circ} 30^{\prime}\) when measured from \(\mathrm{O}\) and is \(1042 \mathrm{~m}\) distant from O. Calculate the distance from the tower to the chimney.

For questions \(1-10\) solve \(\triangle \mathrm{ABC}\) given \(\mathrm{AC}=29 \mathrm{~cm}, \mathrm{BC}=19 \mathrm{~cm}, B=49^{\circ}\)
See all solutions

Recommended explanations on Physics Textbooks

Particle Model of Matter

Read Explanation

Space Physics

Read Explanation

Work Energy and Power

Read Explanation

Wave Optics

Read Explanation

Classical Mechanics

Read Explanation

Dynamics

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.

Sign-up for free