Question

In a right triangle the leg opposite to the acute angle of 30° is 7 in. Find the hypotenuse and other leg.

Answer 1

This is a 30-60-90 triangle.
Therefore,
7 is A
the other leg is A√3
And the hypotenuse is 2A
So the other leg is 7√3 and the hypotenuse is 14

Answer 2

Hypotenuse = 14in

Adjacent = 12.12in

Explanation:

Check attachment for diagram

Using SOH, CAH TOA method

According to SOH

Sin(theta) = Opposite/Hypotenuse

Given theta = 30°

Opposite = 7in

Sin30° = 7/Hypotenuse

Hypotenuse = 7/sin30°

Hypotenuse = 7/0.5

Hypotenuse = 14in

The other leg will be the adjacent say x

Using Pythagoras theorem to get x

Hyp² = Opp²+Adj²

14² = 7²+x²

x² = 14²-7²

x² = 196-49

x² = 147

x = √147

x = 12.12in

The value of the other leg is 12.12