SOLUTION: Find the length of the altitude drawn from the vertex angle of an isosceles triangle if each of its two congruent sides has length 12 and the base angles are 48°. Find the length

Algebra ->  Triangles -> SOLUTION: Find the length of the altitude drawn from the vertex angle of an isosceles triangle if each of its two congruent sides has length 12 and the base angles are 48°. Find the length       Log On


   

Question 867859: Find the length of the altitude drawn from the vertex angle of an isosceles triangle if each of its two congruent sides has length 12 and the base angles are 48°. Find the length to the nearest integer.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
if the base angles are 48 degrees and the sides are 12, then the sin(48) = opposite divided by hypotenuse = altitude divided by 12.
your formula is:
sin(48) = altitude / 12
multiply both sides of this equation by 12 to get:
altitude = 12 * sin(48)
use your calculator to solve for the altitude to get altitude = 8.917 which rounds up to 9.
cos(48) = base of one of the right triangles formed / hypotenuse which is equal to base / 12 which makes base of one of the right triangles formed equal to 12 * cos(48) which makes it equal to 8.03 which rounds down to 8.
this makes the base of the isosceles triangle equal to approximately 16.
everything checks out.
your altitude is equal to 9 rounded to the nearest integer.