Question

what is the exact height of a right triangle with an angle that measures 30 degrees adjacent to a base of 12.

Answer 1

Answer: 6 units

Explanation:

To find the height of the right triangle with an angle that measures 30 degrees adjacent to a base of 12, you can use the formula h = (b x sin(theta)), where h is the height, b is the base, and theta is the angle in radians.

First, convert the angle of 30 degrees to radians by multiplying it by pi/180:

theta = 30 degrees x pi/180 = pi/6 radians

Then, substitute the values into the formula:

h = 12 x sin(pi/6) = 12 x 1/2 = 6

Therefore, the height of the right triangle is 6 units.

Answer 2

Explanation:

For a RIGHT triangle , TanΦ = opposite leg/adjacent leg = height/12

tan 30 = height /12

12 tan 30 = height

12 (sin 30 / (cos 30) = height

12 * 1/2 / (sqrt(3) /2) = height

6 * 2 / sqrt (3) = 12 /sqrt 3 = 4 sqrt 3