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In Exercises $75-84$, round your answer to the nearest tenth where necessary. One leg of a right triangle is 10 in., and the hypotenuse is 26 in. Find the length of the other leg.
the law of signs to find the missing angles and sides of Triangle ABC were given. That angle, see is um measurement of Anglesey is 62 degrees, the measurement of angle A He is 17 degrees and side A is one degree. Now, before we go ahead and start using our laws of sons, we can actually go ahead and find our angle. We know that all three angles of a triangle will add up to give me 180 degrees. Well, we know angle a a 17. We don't know be, but we know angle. See, It's 62 degrees combined. They make 79. So that means that angle B when I said tried 1 80 minus 79 is 101 degrees. By going ahead and doing that, we can definitely go ahead and find our signs quick. Now, since we know angle A inside A, that's gonna be the one law, the one, um, fraction we're gonna use every time. So we're gonna dio son of a divided by a and let's go ahead and let's do see because we're given angle, see, so Sanusi equals C so we can see that son of a It's 17 inside a is one angle, See was 62. So we're gonna do sign of 62 oversee Because that's what we don't know and what we're trying to find. We're gonna cross multiply, so we'll have one sign of 62 equals si sign of 17. We'll divide both sides by sons 17. So that'll leave me. So we're looking for C equals no one times sign of 62 is gonna give me approximately 0.883 and sign of 72 is 0.292 When I divide those, I'm gonna get approximately 3.0 and we're gonna keep it 3.0 right now. This is an approximate. So we're saying that C is approximately 3.0. So now let's find angle B. We're gonna keeps on a over a because we're giving that information. But this time we're gonna look for sign of B over B. Well, we know Sign A is 17/1 time of 17/1 son be. We've already found out what angle B is, and it's 101 degrees over be because that's not what we don't know. So we're gonna cross multiply, so we'll have one. Tom's son of 101 will equal be Tom's son of 17. We'll divide both sides by son of 17. That's gonna leave me beat equals one time sign of 101 is approximately 0.982 and sign of 17 is approximately zero point 292 When I divide those two values again, approximate value of three point four so we can see that B is approximately three point four.