Find BC if line AD is an altitude of <. M<ADC is 14X = 10 degrees. line BD = 2x and line dc is 3X-4
To find the length of BC, we can use the condition that line AD is an altitude of triangle ABC.
We are given that m<ADC (angle ADC) is 14x + 10 degrees and line AD is an altitude. This tells us that angle BAC is 90 degrees (as the altitude is perpendicular to the base).
Now, let's look at triangle ADC. We can use the fact that the sum of angles in a triangle is 180 degrees to find the measure of angle CAD.
m<CAD + m<ADC + m<CDA = 180 degrees
Since m<ADC is given as 14x + 10 degrees and m<CDA is 90 degrees (as it is a right angle), we can substitute these values into the equation:
m<CAD + 14x + 10 + 90 = 180
Simplifying, we have:
m<CAD + 14x + 100 = 180
m<CAD = 80 - 14x
Now, let's consider triangle ABD. We know that the sum of angles in a triangle is 180 degrees. Substituting the given values, we have:
m<BAD + m<ADC + m<A = 180
Since m<ADC is 14x + 10 degrees and m<A is 90 degrees, we can substitute these values into the equation:
m<BAD + 14x + 10 + 90 = 180
Simplifying, we have:
m<BAD + 14x + 100 = 180
m<BAD = 80 - 14x
Since line AD is an altitude, we know that angle BAD and angle CAD are congruent. Therefore, we can set m<BAD equal to m<CAD and solve for x:
80 - 14x = 80 - 14x
0 = 0
This equation has no solution for x, which means that there is no unique value for BC that satisfies all the given conditions.