Oblique Triangles. Back to some good ol' trig. 👍🏿 Different than special triangles, oblique triangles don't really have ways to come up with any of the values for the angles or legs of the triangles by following "shortcuts". You pretty much have to rely on the Law of Sines or Law of Cosines to get the answers to the problems.
To solve this week's problem in completion, you need to recall the following math skills:
✔️ When/How to use the Law of Sines
✔️ When/How to use the Law of Cosines
✔️ How to find the area of an oblique triangle
By the way, you'll need a scientific calculator to help you in computing.
WMP! #19 says...
Happy solving!
Check back on Friday, September 11th for the solution, which will be posted below ⬇️.
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✏️📓 Solution Time! 📓✏️
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Where to start? Well, there is not enough information to solve for any of the unknown angles, B or C. So, we'll solve for the missing side, a. One thing to notice is that the given triangle is not a right triangle, therefore, we cannot use the Pythagorean theorem. That's okay. We'll use something that looks a lot like it--the Law of Cosines formula. We'll use the one that fits our given information.
Now that all the sides are known, we have enough information to solve for the remaining angles, B and C. You have the option to use the Law of Cosines formula again, or you can use the Law of Sines. There's a catch...🤨. Sorry. 🤷🏿 . If you choose to use the Law of Sines, then you will run into a problem solving for angle B. Why?? "A triangle with two sides and a consecutive angle is the ambiguous case of the Law of Sines. In this case, you may have one, two, or no solutions, (Pre-Calculus Workbook for Dummies, Gilman, et al., 2009, p. 179)." Using the Law of Sines to solve for angle C is just fine. If you continue to solve for the remaining angles using the Law of Cosines, you also be fine. What did I do? I used the Law of Sines to solve for angle C.
Now that a second angle has been found, we can easily use subtraction to solve for the last angle:
It's done...the triangle has been solved for! Here's the triangle summary:
The last thing the needs to be done is to find the area of the triangle. Since the height of the triangle cannot be easily seen or found, we will not be using the traditional area formula of a triangle. Here's another formula to find the area of an oblique triangle:
The area can also be found by replacing the sides and angle, accordingly, in the formula. Similar results will be found.
◾️ How did you do in solving this week's problem??
◾️ Comment below with your responses and let me know what you thought about this week's problem.
Up next... WMP! #20❗️
Cheers!
The Younge Lady
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