tan of angles

[dmd20000]

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tan 30 = ?

tan 40 = ?

how do we answer these without a calculator?

 

[sacjumpman]

tan 30 = ?

tan 40 = ?

how do we answer these without a calculator?

tan 30 I would recommend memorizing. sqrt3/3, I believe.

Though if you take a 30, 60, 90 triangle. The angle opposite the 30 = 1, opposite 60 = sqrt3, and opposite 90 is 2. From there you can deduce the tan of 30.

You should probably have the 30, 60, 90 triangle memorized as well.

Just memorize everything for 0, 30, 45, 60, 90 all the way back around to 360. With the way QR has become, you need every advantage to get through problems as fast as possible.

Where did you get tan 40 from?
tan 40... I'm not sure that we would be expected to do this one.

 

[Ocean5]

tan 30 = ?

tan 40 = ?

how do we answer these without a calculator?

Tan is sin/ con
So Sin 30 is 1/2, Cos 30 is square root of 3/2

So Tan 30 is 1/2/ssquare root of 3 / 2
Calculationg this we'll have 2/ 2 times square root of 3. Now bc square root an't be in denominator, we have to simplify this equation and that is the answer.

The same goes for Tan 40

 

[sacjumpman]

Tan is sin/ con
So Sin 30 is 1/2, Cos 30 is square root of 3/2

So Tan 30 is 1/2/ssquare root of 3 / 2
Calculationg this we'll have 2/ 2 times square root of 3. Now bc square root an't be in denominator, we have to simplify this equation and that is the answer.

The same goes for Tan 40

Would you clarify more for tan 40?

I still don't see how we would be able to do this without a calculator. Besides estimating that it is between tan 45 and tan 30.

 

[Streetwolf]

You need a calculator for an exact answer to tan 40.

Could try this though (no guarantees for every situation but this seems to work):

tan 30 ~ 0.577
tan 45 = 1

Quite a leap between 15 degrees... 1-0.58 = 0.42, so about 0.14 every 5 degrees...

So tan 40 would be 0.58 + 0.28 ~ 0.86. Actual answer is ~0.84.