Q33. Solve triangle ABC using the giv... [FREE SOLUTION]

Chapter 13: Q33. (page 707)

Solve triangle ABC using the given measurements if $B = 30 {}^{鈭�}, C = 90 {}^{鈭�}{and} b = 11$ . Round measure of sides to the nearest tenth and measures of angles to nearest degree.

Short Answer

Expert verified

The solution for triangleABC is $a = 19.1, c = 22 and 鈭� A = 60 掳$ .

Step by step solution

Step 1. Write down the given parameters of triangle.

The given triangle ABC is shown below whose parameters are represented as $B = 30 {}^{鈭�}, C = 90 {}^{鈭�}{and} b = 11$ .

Step 2. Calculation.

In triangle ABC, $B = 30 {}^{鈭�}, C = 90 {}^{鈭�}{and} b = 11$ . Therefore, $鈭� A = 60 掳$ by angle sum property.

Now, trigonometric ratios,

$\begin{matrix} \sin B = \frac{b}{c} \\ \sin 30 掳 = \frac{11}{c} \\ c = 11 \csc (30 掳) \\ c = 22 \end{matrix}$

Now, in right triangle ABC by Pythagoras Theorem.

$\begin{matrix} c^{2} = a^{2} + b^{2} 鈥塯颈惫别蝉, \\ 22^{2} = a^{2} + 11^{2} \\ a^{2} = 22^{2} 鈭� 11^{2} \\ a = \sqrt{22^{2} 鈭� 11^{2}} \\ a = 19.1 \end{matrix}$

Step 3. Conclusion.

Thesolution for triangle ABC, is $a = 19.1, c = 22 and 鈭� A = 60 掳$ .

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

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Solve triangle ABC using the given measurements if $B = 30 {}^{鈭�}, C = 90 {}^{鈭�}{and} b = 11$ . Round measure of sides to the nearest tenth and measures of angles to nearest degree.

Short Answer

Step by step solution

Step 1. Write down the given parameters of triangle.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Calculus

Mechanics Maths

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

91影视

Solve triangle ABC using the given measurements if B=30,鈭�C=90and鈭�b=11. Round measure of sides to the nearest tenth and measures of angles to nearest degree.

Short Answer

Step by step solution

Step 1. Write down the given parameters of triangle.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Calculus

Mechanics Maths

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve triangle ABC using the given measurements if $B = 30 {}^{鈭�}, C = 90 {}^{鈭�}{and} b = 11$ . Round measure of sides to the nearest tenth and measures of angles to nearest degree.