Triangle $abc$ has side lengths $ab = 9$, $ac = 10$, and $bc = 17$. let $x$ be the intersection of the angle bisector of $\angle a$ with side $\overline{bc}$, and let $y$ be the foot of the perpendicular from $x$ to side $\overline{ac}$. compute the length of $\overline{xy}$.

Step-by-step explanation:

Consider triangle ABC. Segment AX is angle A bisector. Its length can be calculated using formula

Hence,

By the angle bisector theorem,

So,

and

By the Pythagorean theorem for the right triangles AXY and CXY:

Thus,

Subtract from the second equation the first one:

Hence,

Step-by-step explanation:

The semiperimeter of triangle is , so by Heron's formula, the area of triangle is .

The area of triangle $PRX$ is

.By the angle bisector theorem, we have , so and , which means

.

Then is the height of triangle with respect to base , so , which gives us

.

all the angles opposite to the angle 150 would be 150 and all the angles that are next to 150 are 30 because they equal 180 it you add it up.

step-by-step explanation: