Question

Find value of x in the 30° - 60° - 90° triangle. Give your answer as a simplified radical.

Answer 1

Given :-

• A 30° - 60° - 90° traingle is given to us .
• The perpendicular is 15 units .

To Find :-

• The value of x .

Answer :-

As we can see that the triangle is divided by perpendicular bisector . So , the base gets divided into two equal halves . Here we will have to use the ratio of tan , as ;

`\sf\longrightarrow` tan 60° = 15/x

`\sf\longrightarrow` √3 = 15/x

`\sf\longrightarrow` x = 15/√3

`\sf\longrightarrow` x = √3² * 5/√3

`\sf\longrightarrow` x = 5√3

`\sf\longrightarrow` x = 5 * 1.732

`\sf\longrightarrow` x = 8.66

Hence the required answer is 5√3 or 8.66 units.

Answer 2

• x = 5√3

Explanation:

The property of 30° - 60° - 90° right triangle, side ratios are:

• s : l : h = 1 : √3 : 2

Since side x is opposite to 30° angle, it's the short leg and 15 is the long leg. Use ratios to find the value of x:

• x : 15 = 1 : √3
• x = 15/√3
• x = 15√3/3
• x = 5√3