John and Jeremy are the local names for two lighthouses that guard a particularly dangerous part of the coast. John blinks every
6 seconds and Jeremy blinks every 4 seconds. They blink together at midnight. How many seconds will pass before they blink together again?
1 answer:
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Answer:
Step-by-step explanation:
Refer to the attached image.
A right triangle is considered so when one of its corners are 90°.
If sides a and b are equal in length, then the corners across from them are equal in size as well.
The only way for this to be possible is if both corners A and B(opposite of sides a and b) are 45°.
Pythagorean theorem
This theorem states that the square of a right triangle's long side is equal to the sum of the squares of the shorter sides.
In this case:
but since:
the equation can be solved by replacing a with b in the equation:
Answer:
Step-by-step explanation:
Please refer to the attached diagram. (Apologies if the shading or resolution is a bit off.)
So, we want to find θ.
Since we formed a right triangle, we can use right triangle ratios.
We know the measure of the adjacent side to θ and the hypotenuse.
Therefore, we will use the cosine ratio:
The adjacent side is 2 and the hypotenuse is 15. By substitution:
Now, we will take the inverse cosine of both sides. So:
Use a calculator. Hence:
The angle between the ground and the ladder is about 82.34°.
