Calculating 2 sides of right triangle if you only know the hypotenuse and angle?

Question

I need a formula in the form of

side1 = ...
side 2 = ...

Assume hypotenuse is 5 and anle is 30 degreess

I know the formula is sin(side1/hypotenuse) = 30 ... but I forgot how to extract the side1

Answer 1

Assumptions:
Side 1 - the side opposite the angle
Side 2 - the non-hypotenuse side at the angle

Side 1 = hypotenuse * sin(angle)
Side 2 = hypotenuse * cos(angle)

Answer 2

There are two ways to find out!

One is under Trigonometry which you need the trigonometry tables or calculator to know what sin 30, cos 30s are. So keep them ready and use the formula
(By the way it works for all angles in a right triangle)

sin 30 = side opposite / hypotenuse
cos 30 = side adjacent / hypotenuse

From the formulas,
side opposite (side 1) = 5 (sin 30) = 5 (0.5) = 2.5
side adjacent (side 2) = 5 (cos 30)= 5 (0.866) = 4.33

side 1 = 2.5
side 2 = 4.3
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Second way is under Special Right Triangles, which works for only if you have set of degrees 45, 45, 90 or 30, 60, 90.
Since your angle is 30, we can go for the formula for the set of degrees 30, 60, 90.

Ratio of the sides in the special right triangle 30, 60, 90 is 1: square root of 3 : 2
That means opposite side of angle 30: opposite side of angle 60: opposite side of angle 90.

Lets consider the real measure from the ratio would be
1x, square root of 3 (x) , 2 x

you KNOW the opposite side of 90, which means the hypotenuse = 5.
So now, 2x = 5

1x = 2.5
square root of 3 (x) = 1.732 (2.5) = 4.33 = 4.3

So
side 1 = 2.5
side 2 = 4.3

Answer 3

If both angles are equivalent, you could drop a vertical from the accurate, and it is going to cut up the bottom precisely in 0.5, top? so that you've 2 new triangles. the bottom is two inches, and the perspective is sixty 5 ranges. The tangent of sixty 5 ranges is the ratio of the aspect opposite (the height) over the aspect adjacent (both inch base of the smaller triangle. the height may be 2 tan sixty 5 ranges inches, top? the perfect aspect may be the hypotenuse - and it is the sq. root of the sum of the squares of the different 2 aspects, so it may well be sqrt (4 + (2 tan sixty 5 ranges)^2) So search for the tangent of sixty 5 ranges, and pull out your calculator.

Answer 4

Your formula is wrong. It should be sin 30=(side1/hypotenuse). Therefore side1=hypotenuse*sin 30. Side2=hypotenuse*cos 30. These apply to right-angle triangles only.

Answer 5

The sides of a 30-60-90 triangle are in the ratio 1:root-3:2

So 2.5, 2.5 root-3 (4-ish), 5

I don't know it in general though

Answer 6

30-60-90 triangles are unique, their side lengths are x, x*sqrt 3, 2x

If hypotenuse is 5, then the legs are 2.5 and 2.5 * sqrt 3 (about 4.33)

Answer 7

can also apply Pythagoras Theorem
i fu have one side "a" and the hypotenuse "h"
then the other side "b" is given by
b^2=(h^2-a^2)

Answer 8

for a right angled triangle abc right angled atB
sin-0- =AB/AC
NOW IF AC IS GIVEN SAY 5 AND ANGLE 30 THEN
SIN30=1/2
1/2=AB/5
THEREFORE AB=5/2
YOU HAVE AB AC NOW APPLY PYTHAGORAS THEOREM ABSQ+BCSQ=ACSQ PUT VALUES YOU WILL GET ANSWER

Answer 9

opposite/hyp = sin(30)