Question

in a 30 60 90° triangle giving the long leg equals 12 find the short leg of the triangle and find the hypotenuse of the triangle

Answer 1

in a 30 60 90° triangle giving the long leg equals 12 find the short leg of the triangle and find the hypotenuse of the triangle​

see the attached figure to better understand the problem

Remember that the long leg is opposite to 60 degrees angle

the short leg is opposite to 30 degrees angle

step 1

Find the value of x (short leg)

tan(60)=12/x

solve for x

x=12/tan(60)

remember that

`\tan (60^o)=\sqrt[]{3}`

so

`x=\frac{12}{\sqrt[\square]{3}}=\frac{12\sqrt[]{3}}{3}=4\sqrt[]{3}`

step 2

Find the hypotenuse H

sin(60)=12/H

H=12/sin(60)

Remember that

`\sin (60^o)=\frac{\sqrt[]{3}}{2}`

substitute

`H=\frac{12}{(\frac{\sqrt[]{3}}{2})}=\frac{24}{\sqrt[]{3}}=8\sqrt[]{3}`