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Exercises Trigonometry

Example 5 from Algebra and Trigonometry, 10.1 Non-right Triangles: Law of Sines

Finding the Area of an Oblique Triangle

Find the area of a triangle with sides $a = 90, b = 52,$ and angle $γ = 102° .$ Round the area to the nearest integer.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Using the formula, we have

$\begin{array}{l} Area = \frac{1}{2} a b \sin γ \\ Area = \frac{1}{2} (90) (52) \sin (102°) \\ Area \approx 2289 square units \end{array}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find the area of the triangle given $β = 42°,$ $a = 7.2 ft,$ $c = 3.4 ft .$ Round the area to the nearest tenth.

How did it go?

PreviousFinding the Triangles That Meet the Given Criteria Next Finding an Altitude

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 10.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.