How do you find the angle of a right angled triangle when the hypotenuse and adjacent sides are given?

Question

HYP = 14CM
ADJ = 6CM

this picture should explain

http://img386.imageshack.us/img386/5652/1fc0.jpg

or incase that doesn't work

http://img386.imageshack.us/my.php?image=1fc0.jpg

THANX IN ADVANCE

Answer 1

Use the sine ratio of the angle
So let the size of the angle be A
Then sin A = 6/14
= 3/7
So A = arcsin(3/7)
≈ 25.377°
≈ 25° 23'

Whoops sorry should have been cosine!!!

cos A = 3/7
So A = arccos3/7
≈ 64.623°
≈ 64° 37'

The key word for right angled triangles is SOHCAHTOA ("Sock it to her!!")
SOH →sin(angle) = Opposite / Hypotenuse
CAH →cos(angle) = Adjacent / Hypotenuse
TOA →tan(angle) = Opposite / Adjacent
where the angle is not the right angle (or the adjacent side becomes impossible to uniquely identify since the opposite IS the hypotenuse)

Answer 2

The cosine of an angle is equal to the adjacent side over the hypotenuse. Let's call the angle 'x':
cos x = adj / hyp
cos x = 6 / 14 ≈ 0.4286
So, you need to look at a cosine chart to find out the angle (or use a calculator):
cos 64.62° ≈ 0.4286

So your angle in question is approximately 64.62°

Answer 3

Hi. Just remember Sin = O/H Cos = A/H Tan = O/A .
So use Cos = Adj/Hyp = 6 / 14. Cos 6/14 is your angle. Don't need to look.

Answer 4

you be attentive to between the climate, 29.4 instruments. you be attentive to 2 of the angles, 34 levels and ninety levels. The ninety levels attitude is opposite the hypotenuse. it is not sparkling here (yet would be sparkling interior the question) whether the 34 degree attitude is opposite 29.4 instruments or the different. in case you be attentive to a minimum of one ingredient AND the attitude opposite that ingredient, you need to use the sine rule. you already be attentive to that the attitude opposite the hypotenuse is ninety levels. a over sin A = b over sin B = c over sin C.

Answer 5

From our old friend cheif SOHCAHTOA

cos x=ad/,hyp=6/14=3/7
x=arccos 3/7=64.6°

Answer 6

since u gave 2 sides find the third side(opposite) which will come to be 40cm
now u can use any formula from trigonometry
sin(theta) , cos(theta), or tan(theta) which ever one u like u can use and solve for theta which is the required angle

Answer 7

you take the COS othe the two sides...

6/14....

you will get some small number, a decimal....

then you need to take the inverse cosine and you will be left with degrees.

Answer 8

well, the relationship between HYP and ADJ is:
cos(theta)=ADJ/HYP
so
(theta)=arccos(ADJ/HYP)
or can be written as:
(theta)=cos^1(ADJ/HYP)
plug in numbers:
(theta)=cos^1(6cm/14cm)
=cos^1(.42857)
=64.62

to check your answers, i strongly suggest you visit this site:
http://www.pagetutor.com/trigcalc/trig.html

Answer 9

I don't know, but can't wait to see the answer.......