In Exercises 9–24, solve each triangle. Round lengths to the near...

Question

In Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.a = 3, b = 3, c = 3

Accepted Answer

Hello everybody. I hope you're doing. All right. Today, today we're going to be looking at this question that states find the missing angles of the triangle and express the angle to the nearest degree. Now, they tell us that side P is equal to 24. Side Q is equal to 24 side R is equals to 24. Now, the institute is provided all deal with angles are all referring to the different angles and they're denoted with capital letters, whereas the sides were denoted by lower case letters. So for answer choice, A we have that angle P is equal to 60 degrees. Angle, Q is equal to 60 degrees and angle R is equal to degrees. Answer choice B says that P is equal to 50 degrees, Q is 60 degrees and R is 70 degrees. As a choice C says that P is equal to 70 degrees, Q is 60 degrees and R is 50 degrees. And choice D says that P is equal to 50 degrees, Q is equal to 50 degrees and R is equal to 80 degrees. No. Normally for a question like this where they give us the sides. And we're trying to figure out the angle, we can recall a formula known as the cosine rule where let's say we have cosine of an angle A that will be equal to a fraction where in the numerator will have B squared plus C squared minus A squared, all referring to angles. And that will be divided by. And then the dominator will have two multiplied by B multiplied by C. Now, in our case, let's try to draw a general shape of what a triangle could look like. And we'll assign the side. So let's say we have side P, side Q and side R. And now to assign the angles, we'll just look at the angle opposite of a side. So opposite of side R, we can put angle R and we label the opposite side as the angle R because that angle opens up towards the side. So opposite of se side Q will have angle Q and opposite of side P will have angle P. Now, in this case, they told us that P, side P is 24 units, side Q is 24 units and side R is 24 units. Therefore, we have an equilateral triangle. Now where we have an equilateral triangle, we have the sides are equal to each other. However, this also means that the angles will be equal to each other. So angle P will be equal to angle Q and which will be equal to angle R. Now we know that let's recall that a triangle is equal to 180 degrees. So uh when you add up the angles of a triangle, they will add up to 180 degrees. Therefore, we have that angle, P plus angle, Q plus angle R is equal to degrees. Now, if we just noted that all the angles are equal to each other, we can say that 180 degrees divided by three will be equal to P which is equal to Q, which is equal to R because all three angles are the same. So there is an equal distribution of the angles. Now, what all we have to do now is just divide 180 by three. And we therefore have that angle P is equal to angle, Q is equal to angle R is equal to 60 degrees. So we have that all of the angles will be equal to 60 degrees which matches up with answer choice. A so we see how important it can be for a question like this where we would usually use the cosine rule we can avoid and we can try to do it in a shorter amount of time by knowing the rules of an equilateral triangle where we know that these angles will be the same as well as the sides. So I hope that was helpful. And until next time

In Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.a = 3, b = 3, c = 3

Key Concepts

Triangle Properties

Law of Cosines

Rounding and Precision

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