Heights and Distances — Part 2: Problems with two right-angled triangles: visual lesson, ICSE Class 10 Mathematics

Lesson

Heights and Distances, Part 2

Two angles, one height: the shared side joins two right triangles.

In this lesson you will

The common height links the two triangles.

Concept

Five checks that catch most lost marks.
Check before you finish	Why
Is every angle measured from the horizontal?	a vertical reference gives the complementary angle
Do both triangles use the same height or the same base?	that shared side links the two equations
Same side or opposite sides?	subtract the distances for the same side, add for opposite sides
Is the eye height included?	the angle is measured at the eye
Does the answer look sensible, with units and precision stated?	a taller object from a nearer point means a larger angle

Concept

Both points look at the same top $T$ , so $FT = h$ in both triangles.

Two right triangles $PFT$ and $QFT$ share the height $FT = h$.