/*! 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 3 Find the area of a triangle that... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 3

Find the area of a triangle that has sides of length 2 and 7 , with a 3 radian angle between those sides.

Short Answer

Expert verified
The area of the triangle is approximately \(0.99\) square units.

Step by step solution

01

Calculate the sine of the angle

We are given angle c = 3 radians. Using a calculator or python library, we find the value of sin(3) which is approximately 0.1411.
02

Apply the area formula

Now that we have the value of sin(c), we can use the formula to find the area of the triangle: Area of triangle = 1/2 * a * b * sin(c) In this case, a = 2, b = 7, and sin(c) = 0.1411. Area of triangle = 1/2 * 2 * 7 * 0.1411
03

Calculate the area

Now we simply perform the calculations: Area of triangle = 1/2 * 2 * 7 * 0.1411 = 0.9907
04

Round to an appropriate number of decimal places

As a final step, we'll round our area to 2 decimal places (you may choose a different number of decimal places depending on the accuracy required. In this case, rounding to 2 decimal places: Area of triangle 鈮� 0.99 square units. Therefore, the area of the given triangle is approximately 0.99 square units.

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 a formula for \(\sin (4 \theta)\) in terms of \(\cos \theta\) and \(\sin \theta\).

Give an example of an angle \(\theta\) such that both \(\sin \theta\) and \(\sin (2 \theta)\) are rational.

Show that if \(|t|\) is small but nonzero, then $$\frac{\sin (x+t)-\sin x}{t} \approx \cos x$$

Find constants \(a, b,\) and \(c\) such that $$\sin ^{4} \theta=a+b \cos (2 \theta)+c \cos (4 \theta)$$ for all \(\theta\).

Show that if \(\cos (2 u)=\cos (2 v),\) then \(|\cos u|=\) \(|\cos v|\).
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied 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.