Question

Given that the hypotenuse of this right triangle is 25 cm long and that tan(Θ) = 3

Find the values of x and y, accurate to the nearest tenth.

Answer 1

if tan theta = 3 then you can immediately find theta

so then
sin theta = x/35

you can work out cos theta for yourself

Answer 2

hint - the diagram is misleacing - x is much bigger than y

Answer 3

Since tan theta = opp/adj, \[\Large \tan \theta = \frac{ y }{ x } = 3\]which means y = 3x.

Answer 4

hint - the diagram is misleading - x is much bigger than y

Answer 5

From there you can just use pythagorean theorem a^2+b^2=c^2, \[\Large x^2 + y^2 = 25\] and replace y with 3x.

Answer 6

@MrNood there's no need to solve for theta, that adds inaccuracy.

Answer 7

92

MrNood Mathlete






Medals 0 if tan theta = 3 then you can immediately find theta

so then
sin theta = y/35 hence ypou can get y

you can work out cos theta for yourself
then you can get x

Answer 8

either way is perfectly fine

mine is easier

Answer 9

Oh, hang on. It takes me a few moments to register things sometimes, I'm not ignoring you guys.

Answer 10

you can get theta to umpteen decimal places - and as long as you don't round before using sin and cos then you have sufficient accuracy

Answer 11

\[\Large x^2 + y^2 = 25^2 \]sorry, 25^2 not 25.

replacing y with 3x: \[\Large x^2 + (3x)^2 = 25^2\]then just solve for x, and use y=3x to find y.

Answer 12

Oh, alright. Thanks to both of you, though! It's always good to have multiple ways to work something out, imo. Give me one sec.

Answer 13

and how 'exact' is sqrt (62.5)?

Answer 14

about as exact as tan^-1 (3)

Answer 15

Why would you write it as sqrt 62.5? Why not \[\Large 5\sqrt{\frac{ 5 }{ 2 }}\]

Which is pretty exact. If it had asked for an exact answer, it's a lot messier to write in terms of tan^-1 (3)

Answer 16

It is no more exact

it has an irreducible root - mine has a trig function

Answer 17

Or \[\frac{ 5\sqrt {10}}{ 2 }\]

Answer 18

How is it not more exact?

Answer 19

@deercult
as I said above - both methods are equally valid
and equally good

Answer 20

tan^-1 (3) is irrational
sqrt(10) is irrational

both cannot be expressed 'exactly'

Answer 21

This is exact, but a lot uglier than square roots\[\large y = 25\sin( \arctan (3))\]

Yes, they can be expressed exactly. Square root of 10 is expressed exactly.

Answer 22

Irrational numbers aren't incapable of being expressed exactly...

Answer 23

your argument is not consistent

if sqrt(10) is 'exact' then so is tan^-1 (3)

they both precisely define a number that cannot otherwise be written

Answer 24

My argument was not at all inconsistent.

Answer 25

you have tan t =3, that is y /x =3 or y = 3x
and y^2+x^2 =25^2
solve for y,x
It is not hard, right?

Answer 26

@deercult
our semantics are no use to you - do oyu understand how to solve this?

Answer 27

tan^-1 (3) is irrational
sqrt(10) is irrational


to quote @agent0smith
"Irrational numbers aren't incapable of being expressed exactly..."

Answer 28

Not really, sorry. I'm still having trouble following everything, rip...
It's ok, though. I appreciate y'all trying. I'm having a friend just walk me through it when he can get on.

Answer 29

Yeah, but I was never the one who said to use umpteen decimal places. I actually said a few posts back

"This is exact, but a lot uglier than square roots
y=25sin(arctan(3))"

Answer 30

@deercult
Please ignore the stuff above - in particular since your question asks you to express to nearest tenth

Answer 31

In a trig class, square roots are acceptable as exact answers. Inverse trig functions rarely are, since you can find ways to write them in terms of square roots usually.