In acute triangle ABC, segment AD is an altitude, the measure of angle ADB=2x^2+40, BD=9x-3, and DC=6x+15. Find BC.
If ADB is an altitude, it is perpendicular to BC, and angle ADB is 90 degrees. Therefore
2x^2 + 40 = 90 and x = 5
BC = BD + DC = 15x + 12
This is the fourth question I have answered for you in the last hour.
It is about time you show me some of your work.
Clue for this one:
doesn't the altitude AD hit the base BC at a right angle ??
This one works out sooooo nicely, let me know what you got.
To find the length of segment BC, we can use the fact that the sum of the lengths of the sides of a triangle is equal to the perimeter of the triangle.
In this case, we need to find the lengths of segments AB and AC to calculate the perimeter of triangle ABC.
Given that segment AD is an altitude, it is perpendicular to side BC. Therefore, triangle ADB and triangle ADC are right triangles.
From triangle ADB, we know that the length of BD is 9x - 3.
From triangle ADC, we know that the length of DC is 6x + 15.
To find the length of AB, we can use the Pythagorean theorem in triangle ADB:
AB^2 = AD^2 + BD^2
AB^2 = BD^2 (Since AD is an altitude and the altitude is perpendicular to the base)
AB^2 = (9x - 3)^2
To find the length of AC, we can use the Pythagorean theorem in triangle ADC:
AC^2 = AD^2 + DC^2
AC^2 = DC^2 (Since AD is an altitude and the altitude is perpendicular to the base)
AC^2 = (6x + 15)^2
Once we determine the lengths of AB and AC, we can calculate the perimeter of triangle ABC by adding the lengths of all three sides:
BC = AB + AC + BC
However, at this point, we seem to be missing some information. We need the measure of angle ADB (2x^2 + 40) to find the values of x and compute the lengths of AB and AC.