Question

The longer leg of 30°-60°-90° triangle is 16√3. how long is the shorter leg?

Answer 1

length of the shortest leg is 8 \sqrt{3} units

Answer 2

The length of longer leg is 16 units

Explanation:

Given the longer leg of 30°-60°-90° triangle

we have to find the length of shorter leg.

`\text{Length of longer leg=AB=}16\sqrt3`

we have to find the length of BC i.e the shorter leg as side opposite to smaller angle is shortest.

By trigonometric ratios

`\tan 60^(\circ)=(AB)/(BC)`

`\sqrt3=(16\sqrt3)/(BC)`

`BC=(16\sqrt3)/(\sqrt3)=16units`

Hence, the length of longer leg is 16 units