Given: KL ║ NM, LM = 45, m∠M = 50° KN⊥NM, NL ⊥ LM
Find: KN and KL
So I drew it found that m∠K=90°, m∠LNM=40°, m∠KNL=50°
using the rules of trigonometry, I got:
(NL/45) =tan(50°) and that NL=53.63
I checked it and it was correct so using that I plugged it in as a hyp.: (KN/63.63) =cos(50°), KN=34.47 and when I checked that, it was also correct. So I thought I was on a roll so I pluged in 34.37 as an adj. side: (KL/34.47)=tan(50°) and got KL=41.08. And guess what,it was wrong. ughh. I tried the pythagoren th. instead and got 41.09 (from rounding) and it was still wrong. I got 52.52 once and it was also wrong.
Its KL = 41.082
To find KN and KL, we can use the given information and apply trigonometry. Let's break down the steps:
1. Given that KL ║ NM, we know that angles M and K are right angles (m∠K = 90°).
2. From the given information, we have LM = 45.
3. We also know that LM = NL + ML. Since NL ⊥ LM, angle NLM is a right angle, and NL and ML form a right triangle.
4. Using trigonometry, we can find NL. We have (NL/45) = tan(50°). Solving for NL gives NL ≈ 53.63.
5. Now, let's focus on triangle KNL. We have KN ⊥ NM, so angle KNM is a right angle. We are looking to find KN.
6. Again using trigonometry, we can find KN. We have (KN/NL) = cos(50°). Plugging in the values we know, we get (KN/53.63) = cos(50°). Solving for KN gives KN ≈ 34.47.
7. Now, let's find KL. From the information given, KL is the hypotenuse of the right triangle KNL.
8. We can use the Pythagorean theorem to find KL. We have KL = √(KN^2 + NL^2) = √(34.47^2 + 53.63^2) ≈ 62.52.
Therefore, the approximate values for KN and KL are KN ≈ 34.47 and KL ≈ 62.52.
It seems like you have made some progress in solving the problem, but you are having trouble getting the correct answer for KL. Let's go through the steps together to figure out where the mistake might be.
First, you correctly identified that m∠K = 90°, m∠LNM = 40°, and m∠KNL = 50°.
Next, you used trigonometry to find NL. You correctly set up the equation (NL/45) = tan(50°) and solved for NL, which gave you 53.63. This step is correct.
Then, you attempted to find KN using the equation (KN/63.63) = cos(50°). However, it seems like you made a mistake here. The adjacent side should not be 34.37. Instead, you should use the opposite side, which is NL. So the correct equation should be (KN/53.63) = cos(50°), and you can solve for KN.
Now, to find KL, you attempted to use the equation (KL/34.47) = tan(50°). However, it seems like you made an error in setting up this equation. Since KL is the hypotenuse, you should set up the equation using the opposite side, which is NL. So the correct equation should be (NL/KL) = tan(50°). You can then solve for KL.
If this approach does not give you the correct answer, you can try using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So, you can use this theorem to find KL. The equation would be KL^2 = KN^2 + NL^2. You can substitute the values you have for KN and NL, and solve for KL.
I hope this helps you identify and correct any mistakes in your calculations. Let me know if you have any further questions!
If you did what you typed, I'm not surprised. It should have been
(KN/53.63) = cos(50°)