A plane is located at C on the diagram. There are two towers located at A and B. The distance between the towers is 7,600 feet, and the angles of elevation are given.
a. Find BC, the distance from Tower 2 to the plane, to the nearest foot.
b. Find CD, the height of the plane from the ground, to the nearest foot.
It is a right triangle.
The answer should = 6,122. I just need to know how.
If you look this question on openstudy, you can find the triangle I am talking about, it has a base of 7,600 and a couple degrees of 16 and 24. I solved #a, but I am still stuck on #b. Somebody said "sin24 = cd/bc", but I don't know how to solve it. BC = 15,052, that's all I have.
So I guess it would look like this to begin with?:
sin24 = CD/15,052
Step by step would be the best:)
B=180-24=156
ACB=180-156-16=8
sinA/a=sinC/c, sin16/a=sin8/7600
solve for a
BC=15052 ft
sin(B)=CD/d, sin(24)=x/15052
15052 sin(24)=x
solve for x
CD=1622 ft
@idc I’m confused can you go into more detail
I don't get it can you explain how you got that answer
Ms Sue will you help me with this please. I have the answer but not the steps.
How did you find a part of the assessment?
Well, let's get started with solving for CD, the height of the plane from the ground. We know that sin(24) = CD/BC. But before we tackle that, let's take a moment to appreciate how triangles and angles give us so much trouble. They're like those little math pranksters that just refuse to behave. It's like the triangle is saying, "I'm going to give you some angles, but good luck figuring out the lengths!" Classic triangle humor.
Okay, now back to business. To solve for CD in the equation sin(24) = CD/15,052, we'll need to isolate CD. Here's what we do step by step:
Step 1: Multiply both sides of the equation by BC (15,052) to get rid of that fraction. We get BC * sin(24) = CD.
Step 2: Multiply BC (15,052) by sin(24) to find CD. And this where the magic of math happens. CD = BC * sin(24).
Step 3: Plug in the given value of BC (15,052) into the equation. So, CD = 15,052 * sin(24).
Now, to the best of my calculations, the value of CD should be approximately 6,122. But hey, don't quote me on it! Math can be as unpredictable as a clown juggling flaming torches while riding a unicycle. It's always good to double-check your work and make sure the numbers are correct before committing to an answer.
I hope that helps! Remember, math can be pretty serious, but it's important to have a sense of humor when dealing with it. Let me know if you need any more help or if you want me to tell you another math-related joke!
To solve part (b) of the problem, we need to use trigonometry and the given information about the triangle.
Step 1: Identify the relevant trigonometric ratio:
We are given the angle of elevation of 24 degrees and we are looking for the height CD, which is opposite the angle. So, we will use the sine ratio, as mentioned: sin(24) = CD/15,052.
Step 2: Solve the equation for CD:
To find CD, we need to isolate it. Multiply both sides of the equation by 15,052:
sin(24) * 15,052 = CD
Step 3: Calculate the value:
Using a calculator, find the sine of 24 degrees and multiply it by 15,052:
sin(24) ≈ 0.4067366431
CD ≈ 0.4067366431 * 15,052 ≈ 6,116.851735 feet
Step 4: Round to the nearest foot:
Since the question asks for the answer to the nearest foot, round the value of CD to the nearest whole number. In this case, CD ≈ 6,117 feet.
Therefore, the height of the plane from the ground, CD, to the nearest foot is 6,117 feet.