Question 1041081: Use the following ratios to address the questions below:
a. sin = 1/2
b. sin = 6/13
c. sin = 9/10
d. sin = 12/15
e. cos = 1/2
f. cos = 6/13
g. cos = 9/10
h. cos = 12/15
i. tan = 1/2
j. tan = 6/13
k. tan = 9/10
l. tan = 12/15
1. Use each trigonometric ratio to determine the length of all three sides of each triangle. Did you notice a pattern in the answers? If so, make sure you can explain the pattern.
2. Using similar triangles, calculate the altitude of each triangle. Round your answers to the nearest hundredth, if necessary.
Also, how do you calculate the sine, cosine, and tangent of any angle between 0 and 90 using a calculator or other technology?
Thanks in advance!
Answer by AnlytcPhil(1806)   (Show Source):
You can put this solution on YOUR website!
Use the facts:
to make this chart
opposite adjacent hypotenuse
a. sin = 1/2 1 2
b. sin = 6/13 6 13
c. sin = 9/10 9 10
d. sin = 12/15 12 15
e. cos = 1/2 1 2
f. cos = 6/13 6 13
g. cos = 9/10 9 10
h. cos = 12/15 12 15
i. tan = 1/2 1 2
j. tan = 6/13 6 13
k. tan = 9/10 9 10
l. tan = 12/15 12 15
Then use the Pythagorean theorem to fill in the missing
values for the missing side of the right triangle:
opposite adjacent hypotenuse
a. sin = 1/2 1 √3 2
b. sin = 6/13 6 √133 13
c. sin = 9/10 9 √19 10
d. sin = 12/15 12 √81 = 9 15
e. cos = 1/2 √3 1 2
f. cos = 6/13 √133 6 13
g. cos = 9/10 √19 9 10
h. cos = 12/15 √81 = 9 12 15
i. tan = 1/2 1 2 √5
j. tan = 6/13 6 13 √205
k. tan = 9/10 9 10 √181
l. tan = 12/15 12 15 √369 = √(9*41) = 3√41
The only pattern we can see so far is that the first four opposite
sides are the same as the next four adjacent sides and vice-versa.
Also the first four hypotenuses are the same as the next four hypotenuses.
The last four have the same opposite sides as the first four, and the
adjacents are the same as the hypotenuses in the first four. So let's get
a calculator and round them off to the nearest hundredth and see if we can
see any other patterns:
opposite adjacent hypotenuse
a. sin = 1/2 1 1.73 2
b. sin = 6/13 6 11.53 13
c. sin = 9/10 9 4.36 10
d. sin = 12/15 12 9.00 15
e. cos = 1/2 1.73 1 2
f. cos = 6/13 11.53 6 13
g. cos = 9/10 4.36 9 10
h. cos = 12/15 9.00 12 15
i. tan = 1/2 1 2 2.24
j. tan = 6/13 6 13 14.32
k. tan = 9/10 9 10 13.45
l. tan = 12/15 12 15 19.21
There is no other pattern except those same ones.
2. Using similar triangles, calculate the altitude of
each triangle. Round your answers to the nearest hundredth,
if necessary.
Since they are all right triangles their altitudes are
the same as their opposite sides. No need for similar
triangles.
Also, how do you calculate the sine, cosine, and tangent
of any angle between 0 and 90 using a calculator or other
technology?
On a calculator to find the sine, you put the opposite side in
the calculator, press the division key, then put in the
hypotenuse and press the = or enter key.
On a calculator to find the cosine, you put the adjacent side in
the calculator, press the division key, then put in the
hypotenuse and press the = or enter key.
On a calculator to find the tangent, you put the opposite side in
the calculator, press the division key, then put in the
adjacent and press the = or enter key.
[In my opinion, this is a silly problem!]
Edwin
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