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Chapter 6

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01:45

If the cosine of the large…

00:21

Find the sine of the small…

01:36

Solve each triangle. Round…

00:51

In a triangle, the measur…

In $\triangle A B C, \angl…

02:21

02:15

01:46

For each triangle, find th…

01:09

In $15-20,$ find, to the n…

02:08

Okay, this one says, What is the coastline of the smallest angle in a right triangle, whose small aside is five and whose high partners is ten. Let's go and start by making some sort of a visual representation for the situation, so we know we have a right triangle. I can. And then we know that the smallest side is five. The high pop news, which is always along the side because ten. So then we want to know the coastline of the smallest angle, and we always know that the opposite the angle that's opposite to the smallest side is always going to be the smallest angle. So similarly to how this ninety degree angle is the largest out of the three angles in the triangle, and it has the largest site. So then the opposite angle to five is going to be right here until what? We're going to go ahead and call that data. So then we know from Soca Tura that co sign I was going to be the adjacent over the hype brightness. So if we know it's going to be the Jason over the high part news, we know that we want to find this value right here because this wanna see Jason and we do already have the high pot news. So then we can say adjacent over ten. So in order to find the adjacent, we can use the Pythagorean theorem pokery him, they're which says a squared plus B squared is equal to C squared. And you can use this to find any missing side whenever you have a right triangle. So then we know that five squared plus b squared there's going to be ten squared, and that's nicely for B weaken First attract by five squared on both sides and then that gives us B squared is equal to one hundred minus twenty five because ten squared is one hundred and five squared is twenty five. So we know that B squared is seventy five. Then, in order to isolate the B because we want to get alone as opposed to having the square, we're gonna take the square root of both set. So then this square in the square root are gonna cancel out on we'LL get B is equal to the square root of seventy five. So then over here we can say this is squared of seventy five, which means even for our coast on equation right here, you can put that back in to say that the square root of seventy five over ten should be our co sign, which is going to become zero point eight six six, then that should be our final answer.

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