Which 30°-60°-90° triangle is labeled with the correct side length ratio?
2 answers:
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Answer: approximately 5148 feet directly north of point A
This is equivalent to 0.975 miles
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Explanation:
Check out figure 1 (attached image below) to see how the drawing is set up.
Points A and B are separated by 2 miles, or 10560 feet. Use the conversion factor 1 mile = 5280 feet.
Because sound travels at roughly 1100 feet per second (assuming all of the conditions are right), this means that after x seconds, the sound wave has traveled a total distance of 1100x feet. This is the distance from A to C. Point C is the firework location.
The distance from B to C is 1100(x+6) feet because it takes 6 more seconds for the soundwave to travel from C to B, compared from C to A.
Note that triangle ABC is a right triangle. The 90 degree angle is at point A.
We can use the pythagorean theorem to solve for x
See figure 2 in the attached images to see the steps on solving for x. The numbers get quite big, though in the end x is fairly small. We end up with x = 4.68, which is approximate due to the 1100 figure being approximate.
This means the sound wave takes about 4.68 seconds to go from point C to point A.
With this x value, we can compute the expression 1100x to get
1100*x = 1100*4.68 = 5,148 feet
To convert this to miles, divide by 5280
(5148)/(5280) = 0.975
Therefore,
5148 feet = 0.975 miles
Answer:
4.8 inches
Step-by-step explanation:
Given: The largest frog in the world is goliath which is 12 inches long.
The smallest frog is about 2.5 as long as the goliath.
Lets assume the length of smallest frog be "x".
As given, smallest frog is about 2.5 as long as the goliath.
∴ we can form equation as
Solving the equation to find the value of x
Dividing both side by 2.5
⇒
∴
Hence, the length of smallest frog is 4.8 inches.