Concept 9.4
Two Observations, One Height
Source: NCERT Mathematics, Class 1012 minute lesson
Formal statement
When an object is observed from two points, write one trigonometric equation for each observation. The common unknown, usually the height, links the two equations.
The intuition
From one point the top of a tower is at 60°; walk 20 m back and it is at 30°. Two triangles, sharing one vertical side: the height h.
Write tan 60° = h/x and tan 30° = h/(x + 20). Both contain h, so √3·x = (x + 20)/√3, giving x = 10 m and h = 10√3 m.
The attention
Look at what the two triangles share: the height.
tan 60° = h/x, tan 30° = h/(x + 20)
Look hereNot here
- Look here
- h, the side both triangles share. h appears in both equations. Express it twice and set the expressions equal.
- Not here
- x, the unknown distance. x is unknown too, but the second triangle's base is x + 20, not x. Working on x triangle by triangle goes in circles.
- What it teaches
- With two unknowns and two pictures, find what the pictures have in common.