Solve each right triangle. When two sides are given, give angles ...

Question

Solve each right triangle. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2.

Accepted Answer

Hey, everyone in this problem, we're asked to find the missing sidelines and the missing angle of the right triangle. So the triangle, we're given triangle pr Q, the right angle is that angle Q we're told that side P is 32.8 m and angle P is 26 degrees and 25 minutes. We're given four answer choices. A through D each containing a different value for the missing angle. R and the missing sides. Q and R I know we're gonna come back to these answer choices as we work through the problem. And let's start by finding the missing angle R. And so we're gonna start by finding the missing angle R. We're gonna choose to find that missing angle first because it's gonna be the simplest thing to find. We already know two of the other angles in our triangle. And so the key here is to recall that the angles of a triangle. So R plus P plus Q add up to 180 degrees. Yeah, R is the angle we're looking for. So we have R plus P were given in the diagram 26 degrees in 25 minutes plus angle Q, which is our 90 degree angle. OK. This equals 180 degrees. We can subtract 90 degrees from both sides. We can subtract 26 degrees and 25 minutes from both sides. And we're gonna be left with angle R being equal to 63 degrees and 35 minutes. And so we've done part one, we found the missing angle in this triangle. And if we take a look at our answer choices, option A has that this angle R is exactly 63 degrees and that is not what we found. So we can eliminate option A options. BC and D have that, that angle is 63 degrees in 35 minutes just like we found. So all of those are potential choices. I guess we're down to three answer choices and we have these two side lengths to figure out now. OK? So let's go ahead and start by looking at side length R. And when we're looking for side length R, we know angle P, we know side P which is opposite to it and side R is the adjacent side. OK. So we wanna choose the trigonometric ratio that relates the opposite and the adjacent sides and that's gonna be tangent. And because we have this right angle triangle, we can use these trigonometric ratios. And so we have that tangent of the angle P again, it's gonna be equal to the opposite side divided by the adjacent side. We know that the angle P is 26 degrees and 25 minutes. The tangent of 26 degrees and 25 minutes is going to be equal to the opposite side, which were given in the diagram as 32.8 m divided by the adjacent side, which is that side R we're looking for now, we can rearrange our equation R is going to be equal to 32.8 m divided by tangent of 26 degrees and 25 myths. When we work this out on our calculator, we get that R is approximately equal to 66.027 meters. So we figured out side length are now we're gonna go back to our answer choices. Once again, answer choice B has the R is 73.7 m. This is not what we found. So we can eliminate answer choice B options, C and D have 66 m, which is what we found. And so those could be potential solutions. So we're gonna leave those answer choices and we're gonna get to our very last calculation which is finding the second missing side or side Q. Now, for side Q, we're gonna use angle P. OK. So we have angle P, we know the opposite side. And now we're interested in finding the hypotenuse, we're gonna use our trigonometric ratios again. But instead of tangent, this time, we're gonna be using a sun. And so we know that sine of our angle P is going to be equal to the opposite side divided by the hypotony. Substituting in what we know we have sign of 26 degrees and 25 minutes is going to be equal to 32.8 m divided by side, Q. Again, we can rearrange inside Q is going to be equal to 32.8 m divided by s of 26 degrees in 25 minutes. And when we work this out, we get that Q is going to be equal to approximately 73.7 to 5 m. Ok. So that is the second missing sideline. We had narrowed it down to two answer choices and now we can see that the correct answer is going to be option C and the missing angle was 63 degrees and 35 minutes missing side Q 73.7 m and missing side R 66 m. Thanks everyone for watching. I hope this video helped you in the next one.

Solve each right triangle. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2.

Key Concepts

Right Triangle Properties

Trigonometric Ratios

Angle Measurement in Degrees and Minutes

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