In a right triangle the leg opposite to the acute angle of 30 degrees in 7in. find the hypotenuse and the other leg plz show work

hypotenuse = 14inches

The other leg {adjacent} = 12.12inches

Step-by-step explanation:

To find the hypotenuse and the other leg which would be the adjacent of the triangle given the opposite to be 7inches, with opposite angle given as 30.

See attachment for illustration.

Therefore to find the hypotenuse we will apply the sine rule which says

a/sineA = b/sineB

Where a is line and A is its opposite angle same as b is line and B is its opposite angle.

So in this case:

a= 7inches, A = 30° , b = hypotenuse, B = 90° (angle at right angle).

Therefore we have,

7/sine30 = hypotenuse/sine90

Cross multiple

Hypotenuse*sine30 = 7*sine90

Hypotenuse = 7*sine90/sine30

Hypotenuse = 7*1/0.5

Hypotenuse = 7/0.5 = 14inches

Hypotenuse = 14 inches

Having gotten hypotenuse we can now find the other leg {adjacent} using the Pythagoras theorem, which says

Hypotenuse² = opposite² + adjacent²

adjacent² = Hypotenuse² - opposite²

adjacent² = 14² - 7²

adjacent² = 196 - 49

adjacent² = 147

adjacent = √147

adjacent = 12.1244 ~ 12.12inches