Question

If the hypotenuse of a 30-60-90 triangle has length 15, then the shorter leg has length

Answer 1

Step-by-step explanation:

Given : If the hypotenuse of a 30-60-90 triangle has length 15 then the shorter leg has length  5.5 , 6.5 , 7.5.

To find : What is the length of the other leg and hypotenuse ?

Solution :

For a  30-60-90 triangle, sides are in the ratio  $1:\sqrt{3}:2$

where, 1 is the shorter side,  

$\sqrt{3}$ the other side

and 2 the hypotenuse.

Short leg = 5.5

Other leg = $5.5\times \sqrt3=5.5\sqrt3$

Hypotenuse = $5.5\times 2=11$

Short leg = 6.5

Other leg = $6.5\times \sqrt3=6.5\sqrt3$

Hypotenuse = $6.5\times 2=13$

Short leg = 7.5

Other leg = $7.5\times \sqrt3=7.5\sqrt3$

Hypotenuse = $7.5\times 2=15$