I dont know how to use trig to find length of triangle sides?

Question

If I have all all the angle measurements how do I find the side length measurements. for instance i have a 30 60 90 triangle with the short side is 9 ft long. How can i use trig to find the other two sides. I know SOHCAHTOA but i am not sure how to use it.

Answer 1

Well we already know that in a 30 60 90 triangle the short side is half of the hypotenuse=18 and the long side is the short side * √3, but to use trig to find it then remember the side opposite and angle over the hypentuse is = sin function
short side/hyp = sin 30
9/hyp=.5
hyp = 18
then long side/hyp = sin 60
long side = 18*√3/2

Answer 2

The method is:

draw the triangle,
label the sides and angles (angles: A, B, C; sides: a, b, c)
substitute the known values for angles and sides

You now have a good visual of what needs to be calculated

write down your formulas
substitute the known values
calculate as necessary to find unknowns

With practice, you will be able to skip the basic steps to get to deciding which formulas you need to calculate the unknowns.

Angles:
A=30
B=60
C=90

Lengths:
opposite side = a = 9ft
adjacent side = b = ?
hypotenuse = c = ?

A way of remembering how to compute the sine, cosine, and tangent of an angle.

SOH stands for Sine equals Opposite over Hypotenuse
(or: Sin A = a/c)

CAH stands for Cosine equals Adjacent over Hypotenuse (or: Cos A = b/c)

TOA stands for Tangent equals Opposite over Adjacent
(or: Tan A = a/b)

So, the formulas are:

Pythagorean theorem: a^2 + b^2 = c^2.
Substitute known values: 9^2 + b^2 = c^2

Sines:
sin A = a / c
sin B = b / c

Substitute known values:
sin 30 = 9/c
sin 60 = b/c

Cosines:
cos A = b / c
cos B = a / c

Substitute known values:
cos 30 = b / c
cos 60 = 9 / c

Tangents:
tan A = a / b
tan B = b / a

Substitute known values:
tan 30 = 9 / b
tan 60 = b / a

Now you can begin.

find c:

sin 30 = 9 / c
c x sin 30 = 9
c = 9 / sin 30
c = 9 / 0.5
c = 18

OR:

cos 60 = 9 / c
c x cos 60 = 9
c = 9 / cos 60
c = 9 / 0.5
c = 18

find b:

9^2 + b^2 = 18^2
b^2 = 18^2 - 9^2
b^2 = 324 - 81
b^2 = 243
b = sq rt 243
b = 15.588457268119896
b = 15.59 (rounded down to decimal places)

OR:

tan 30 = 9 / b
b x tan 30 = 9
b = 9 / tan30
b = 15.588457268119896
b = 15.59 (rounded down to decimal places)

So, your values are:

Angles:
A=30
B=60
C=90

Lengths:
a = 9ft
b = 15.59ft
c =18ft

Answer 3

Sin A = opposite side /hypotenuse
In triangle angle opposite to smallest side is the least
because 9 is the shortest side, 30 degrees is its opposite angle
Sin 30 = 9/hypotenuse
hypotenuse = 9/sin 30
= 9/1/2 (since sin 30 = 1/2)
= 18 ft
similarly sin 60 = opposite side to angle 60/hypotenuse
since sin 60 = sqrt(3)/2
sqrt(3)/2 = [opposite side (to angle 60)] /18
opposite side (to angle 60) = 18(sqrt(3)/2
=9(sqrt(3)
= 9(1.732)
=15.58 ft
So the three sides are 9 ft, 15.58 ft and 18 ft

Answer 4

Sin A = opposite side /hypotenuse
In triangle angle opposite to smallest side is the least
because 9 is the shortest side, 30 degrees is its opposite angle
Sin 30 = 9/hypotenuse
hypotenuse = 9/sin 30
= 9/1/2 (since sin 30 = 1/2)
= 18 ft
similarly sin 60 = opposite side to angle 60/hypotenuse
since sin 60 = sqrt(3)/2
sqrt(3)/2 = [opposite side (to angle 60)] /18
opposite side (to angle 60) = 18(sqrt(3)/2
=9(sqrt(3)
= 9(1.732)
=15.58 ft

Answer 5

based on your given data, for example, 9 is the shortest side of the triangle which means that it is opposite of the smallest angle that is 30 degrees.using SOHCAHTOA, particularly SOH (sine of angle = side opposite the angle / the hypotenuse) you can obtain the other sides:

sine of 30* = 9 / hyp.
1/2 hyp. = 9
hyp. = 9/ 1/2
hyp. = 18
(*sine of 30 = 1/2)

then solving for the adjacent side, use CAH (cosine of angle = adj. side / hyp.)

cosine 30 = adj. side / 18
sq. root of 3 over 2 = adj. / 18
adj. side = 9 times sq. root of 3

you may use calculator for the sine and cosines.

hope this helps.

Answer 6

The hypotenuse = 2 times the Short leg = 18
The long leg = sqrt(3) times short leg = 9*sqrt(3).

Forget SOHCAHTOA