Solve each problem. (Source for Exercises 49 and 50: Parker, M., ...

Question

Solve each problem. (Source for Exercises 49 and 50: Parker, M., Editor, She Does Math, Mathematical Association of America.)

Create a right triangle problem whose solution can be found by evaluating θ if sin θ = ¾.

Accepted Answer

Hello, today we're going to be drawing a valid right triangle for which sine theta is equal to five divided by 13. So we are told that the trigonometric value sine theta is equal to five divided by 13. So how can we use this information to draw a valid right triangle for this trigonometric function? Well, if we recall the identity for sine, we are told that sine of theta is equal to the opposite side of a right triangle divided by its hypotenuse. So we know that there are three parts to a right triangle. A right triangle has a right degree angle which is equal to degrees. We have the two shorter legs and we have the longer side which is considered the hypotenuse. So let's go ahead and allow this angle here to be our generic angle theta. Now, if we take a look at the given sine function, the sine function is equal to five divided by the 13. This means that the opposite side to theta will equal to five and the hypotenuse will equal to 13. So we can label that side with respect to theta. The opposite side to theta will be the height of this right triangle. And we know that that measurement is going to be five. And we know that the hypotenuse is going to be 13. And the hypotenuse is the longest side of the right triangle. So this side of the right triangle will equal to 13. Finally, we need to find the missing side length of this right triangle. We can use the Hy Pythagorean theorem to help us find this missing missing length. Now, the Pythagorean theorem states that C squared is equal to A squared plus B squared C represents the hypotenuse and A and B represents the two side links. We're going to allow the unknown side to be A but we do know that C is equal to 13 and B is equal to five. So we can say that 13 squared is equal to A squared plus five squared, 13 squared will give us the value of A squared will remain the same, but five squared will evaluate to give us 25. In order to solve for a, we're going to subtract 25 to both sides of the equation. This will leave us with A squared is equal to 144. And in order to solve for A, we're going to take the square root of both sides of this equation leaving us with A is equal to 12. That means that the missing side length to this right triangle. Is going to be 12 and to summarize the right triangle with side links 12 and five and a hypotenuse of will allow sine data to equal to five divided by 13. And this is going to be the solution to this problem. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

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Solve each problem. (Source for Exercises 49 and 50: Parker, M., Editor, She Does Math, Mathematical Association of America.) Create a right triangle problem whose solution can be found by evaluating θ if sin θ = ¾.