kayden paddled a canoe to an island. the island is 8 miles from the shore. his trip to the island took two hours while paddling
1 answer:
Answer:
Step-by-step explanation:
GIVEN: kayden paddled a canoe to an island. the island is miles from the shore. his trip to the island took two hours while paddling against the current. he paddles
mph with no current.
TO FIND: what was the speed of the current.
SOLUTION:
distance of island from the shore miles
total time taken by Kayden hours
speed of Kayden in still water
Let the speed of current be
Speed of Kayden against current
As,
Hence speed of current is
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Answer:
Answer d)
,
, and
Step-by-step explanation:
Notice that there are basically two right angle triangles to examine: a smaller one in size on the right and a larger one on the left, and both share side "b".
So we proceed to find the value of "b" by noticing that it the side "opposite side to angle 60 degrees" in the triangle of the right (the one with hypotenuse = 10). So we can use the sine function to find its value:
where we use the fact that the sine of 60 degrees can be written as:
We can also find the value of "d" in that same small triangle, using the cosine function of 60 degrees:
In order to find the value of side "a", we use the right angle triangle on the left, noticing that "a" s the hypotenuse of that triangle, and our (now known) side "b" is the opposite to the 30 degree angle. We use here the definition of sine of an angle as the quotient between the opposite side and the hypotenuse:
where we used the value of the sine function of 30 degrees as one half:
Finally, we can find the value of the fourth unknown: "c", by using the cos of 30 degrees and the now known value of the hypotenuse in that left triangle:
Therefore, our answer agrees with the values shown in option d)