Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 7 - Applications of Trigonometry and Vectors - Section 7.1 Oblique Triangles and the Law of Sines - 7.1 Exercises - Page 304: 53


$356$ cm$^{2}$

Work Step by Step

The area of the triangle is half the product of the length of two sides and the sine of the angle included between them: $Area=\frac{1}{2}ac \sin B$ We substitute the values of $a,B$ and $c$ in this formula and solve: $Area=\frac{1}{2}ac \sin B$ $Area=\frac{1}{2}(30.4)(28.4) \sin 124.5^{\circ}$ $Area=\frac{1}{2}(863.36) \sin 124.5^{\circ}$ $Area=431.68 \sin 124.5^{\circ}$ Using a calculator, $\sin 124.5^{\circ}=0.8241$. Therefore, $Area=431.68 \sin 124.5^{\circ}$ $Area=431.68(0.8241)$ $Area=355.75\approx356$ Therefore, the area of the triangle is $356$ cm$^{2}$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.