A base angle of an isosceles triangle measures 30, and the length of one of the legs is 12. What is the length of the altitude drawn to the base of the triangle?

The altitude of the given isosceles triangle is 6 units.

Given information:

A base angle of an isosceles triangle measures 30, and the length of one of the legs is 12.

Let h be the altitude of the triangle. The altitude, half base, and one leg of the triangle will make a right triangle with base angle of 30 degrees.

So, use the trigonometric ratios to find the value of altitude as,

Therefore, the altitude of the given isosceles triangle is 6 units.

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6

Step-by-step explanation:

From the question, a base angle of isosceles triangle is 30°.We are also informed that one of the legs is 12. The altitude is opposite to the angle having a measure of 30°. The hypoteneous in the right angled triangle which is formed by drawing the altitude is 12. This will be calculated as:

Sin = opposite/hypotenuse

Sin 30°=length of the altitude/12

Note that sin 30° = 0.5

0.5 = length of the altitude/12

length of the altitude = 12 × 0.5

Hence, length of altitude = 6