1. In triangle DEF, m angle D=45, m angle E=63, and EF=24 in. What is DE to the nearest tenth of an inch?
A) 30.3 in.
B) 15.1 in.
C) 32.3 in.
D) 10.5 in.
Is the Answer A?
I'm not quite sure though since i'm confused on this question. If someone could help that would mean so much, thank you!
since the angles add to 180°, angle F is 72°.
Using the law of sines,
DF/sin72° = 24/sin45°
x = 32.28
So, did you just guess at A?
so its c?
It was extremely close, there was no guessing. I saw someone else do this problem and got A, but did not explain it well.
Thx Steve!
Well, well, well, it seems like we have a triangle on our hands! So, you're looking for the length of DE, huh? Let's see what we can do here.
You're given that angle D measures 45 degrees, and angle E measures 63 degrees. Those are some fancy angles, but how do they help us? Well, my friend, we can use the law of sines to solve this. That's right, the math gods have bestowed upon us a theorem!
The law of sines states that the ratio of the length of a side of a triangle to the sine of the opposite angle is the same for all three sides. Fancy, isn't it?
Anyway, let's apply this theorem. We have angle D and angle E, and we need to find the length of side DE, so we'll use the sin of angle E. We can set up an equation like this:
DE / sin(E) = EF / sin(D)
Now, let's plug in the values we know. We have EF = 24 inches, angle E = 63 degrees, and angle D = 45 degrees. Doing some calculations, we get:
DE / sin(63) = 24 / sin(45)
Now, solve for DE, my friend. Punch those numbers into your calculator and you'll find that DE is approximately 32.3 inches.
So, the answer to your question is C) 32.3 inches. Well done, my friend! Keep that geometry game strong!
To find the length of DE in triangle DEF, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant. In other words, we can use the formula:
DE / sin(D) = EF / sin(E)
Substituting the given values, we have:
DE / sin(45°) = 24 in / sin(63°)
The sine of 45° is √2 / 2, and the sine of 63° is approximately 0.891. Hence, we can rewrite the equation as:
DE / (√2 / 2) = 24 in / 0.891
Simplifying further:
DE = (24 in * √2 / 2) / 0.891
Using a calculator, we get:
DE ≈ 15.1 in
Therefore, the answer is option B) 15.1 in.