Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Problem 10

In questions \(1-10\) solve \(\triangle \mathrm{ABC}\) given \(\mathrm{AB}=80 \mathrm{~cm}, \mathrm{BC}=70 \mathrm{~cm}, \mathrm{AC}=62 \mathrm{~cm}\)

Short Answer

Expert verified
Question: Given a triangle with side lengths a = 80 cm, b = 70 cm, and c = 62 cm, find all angles of the triangle. Answer: To find all the angles in the given triangle, follow the steps outlined in the solution. First, use the Law of Cosines to find angle C. Next, use the Law of Sines to find angle B. Finally, use the fact that the sum of angles in a triangle is 180 degrees to find angle A.

Step by step solution

01

Calculate angle C using the Law of Cosines

The Law of Cosines states that for any triangle with sides a, b, and c, and angle C opposite side c, we have: \[c^2 = a^2 + b^2 - 2 \cdot a \cdot b \cdot cos(C)\] We can plug in the given values for a, b, and c, i.e., a = 80 cm, b = 70 cm, and c = 62 cm, and then solve for angle C: \[62^2 = 80^2 + 70^2 - 2 \cdot 80 \cdot 70 \cdot cos(C)\] Now, we can solve for cos(C): \[cos(C) = \frac{80^2 + 70^2 - 62^2}{2 \cdot 80 \cdot 70}\]
02

Find the angle C

Now compute the value of cos(C) and use inverse cosine to find the angle C: \[C = cos^{-1}\left(\frac{80^2 + 70^2 - 62^2}{2 \cdot 80 \cdot 70}\right)\]
03

Find angle B using the Law of Sines

The Law of Sines states that for any triangle with sides a, b, and c, and angles A, B and C, we have: \[\frac{a}{sin(A)} = \frac{b}{sin(B)} = \frac{c}{sin(C)}\] We can use this relationship to find angle B: \[\frac{70}{sin(B)} = \frac{62}{sin(C)}\] Now, solve for sin(B): \[sin(B) = \frac{70 \cdot sin(C)}{62}\]
04

Calculate angle B

Compute the value of sin(B) and use inverse sine to find the angle B: \[B = sin^{-1}\left(\frac{70 \cdot sin(C)}{62}\right)\]
05

Calculate angle A

Finally, we can compute angle A using the fact that the sum of angles in a triangle is always 180 degrees: \[A = 180 - B - C\] Now we have calculated all three angles of triangle ABC, and the triangle is solved.

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 1-11 \(\Delta \mathrm{ABC}\) has a right angle at \(\mathrm{C}\). Calculate \(\mathrm{AB}\) given \(\mathrm{AC}=12 \mathrm{~cm}\) and \(A=57^{\circ}\).

For questions \(1-10\) solve \(\triangle \mathrm{ABC}\) given \(A=37^{\circ}, B=47^{\circ}, \mathrm{AB}=17 \mathrm{~cm}\)

A ship travels on a bearing of \(40^{\circ} 00^{\prime}\) for \(12 \mathrm{~km}\) and then changes to a bearing of \(270^{\circ}\) and travels for \(30 \mathrm{~km}\). Calculate (a) the distance of the ship from its starting point (b) the bearing the ship must take to return to its starting position.

For questions \(1-10\) solve \(\triangle \mathrm{ABC}\) given \(\mathrm{AB}=15 \mathrm{~cm}, \mathrm{AC}=23 \mathrm{~cm}, B=57^{\circ}\)

In questions 1-11 \(\Delta \mathrm{ABC}\) has a right angle at \(\mathrm{C}\). Calculate \(A\) given \(\mathrm{AC}=14 \mathrm{~cm}\) and \(\mathrm{BC}=9 \mathrm{~cm}\)
See all solutions

Recommended explanations on Physics Textbooks

Engineering Physics

Read Explanation

Geometrical and Physical Optics

Read Explanation

Mechanics and Materials

Read Explanation

Linear Momentum

Read Explanation

Fundamentals of Physics

Read Explanation

Fields in Physics

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