Finding height of new triangle created by parallel hypotenuse?

[escribblings]

Assuming a right triangle of any size where we know the all lengths and angles.

If we draw a line parallel to the hypotenuse, where the only measurement we know is the distance between the hypotenuse and the new line.

Assuming this new line extends to the x and y axis and therefore making a larger version of the original triangle, how can we find the new lengths of all 3 sides?

For example,

I have a triangle with a base of 120cm and angles of 15°, 75° and 90°

That gives a height for side a of 32.154cm and a hypotenuse of 124.233cm.

Our new line, parallel to the hypotenuse, is spaced 10cm from the hypotenuse (outside the triangle) and its ends extend to meet the x and y axis of the original triangle and so therefore having the same angles.

How do I now find the new height for side A?

 

[escribblings]

Find size of new right triangle from parallel hypotenuse.

If we have a right triangle where we know all it's sides and angles, and we then draw a line parallel to the hypotenuse that extends to intersect with the lines that would continue from the other 2 sides of the triangle, thereby creating a new, larger triangle with the same angles as the first but with unknown lengths for all 3 sides.

How do we find the dimensions for the new triangle if all we have are the dimensions for the old triangle, it's angles and the distance between the hypotenuse and the parallel line?

 

[stapel]

One method might be to work algebraically.

Draw the triangle with the right angle at the origin. Draw the two legs along the positive x- and y-axes; the hypotenuse then is in the first quadrant.

Since you know the lengths of the legs, you know the coordinates of the other two vertices. Use this information to find the slope of the line containing the hypotenuse. Then find the slope of the perpendicular line. Find the equation of the perpendicular line passing through the origin (and thus intersecting the triangle at its right angle).

With this information, use the Distance Formula find the point "n" units past the current hypotenuse. Then, with this point and the original slope, find the equation of the new (larger) triangle's hypotenuse.

Then use this information to find the new x- and y-intercepts, which will tell you the new leg-lengths.

 

[Ishuda]

Assuming a right triangle of any size where we know the all lengths and angles.

If we draw a line parallel to the hypotenuse, where the only measurement we know is the distance between the hypotenuse and the new line.

Assuming this new line extends to the x and y axis and therefore making a larger version of the original triangle, how can we find the new lengths of all 3 sides?

For example,

I have a triangle with a base of 120cm and angles of 15°, 75° and 90°

That gives a height for side a of 32.154cm and a hypotenuse of 124.233cm.

Our new line, parallel to the hypotenuse, is spaced 10cm from the hypotenuse (outside the triangle) and its ends extend to meet the x and y axis of the original triangle and so therefore having the same angles.

How do I now find the new height for side A?

You don't. You don't have enough information. As an example, let's take your triangle with its base of 120cm. First put the left hand point of the base at (0,0). Now you have enough information. However, under the conditions stated, the left hand point of the base might be at (1000,1000) and you would have enough information to solve the problem. However, the answer would be very different than that where the left hand point of the base were at (0,0).

EDIT: I now see your second post does the equivalent of putting the left hand point of the base at (0,0). Now you have enough information and a couple of good hints.