Measuring height of a tree using trigonometric ratios.This experiment

1.	Measuring height of a tree using trigonometric ratios.This experiment can be conducted on a clear sunny day. Look at the figure given above. Height of the tree is QR, height of the stick is BC. Thrust a stick in the ground as shown in the figure. Measure its height and length of its shadow. Also measure the length of the shadow of the tree. Using these values, how will you determine the height of the tree?
Answer» Rays of sunlight are parallel. So, ∆PQR and ∆ABC are equiangular i.e., similar triangles. Sides of similar triangles are proportional. ∴ \(\frac{OR}{BC}\) = \(\frac{PR}{AC}\) ∴ Height of the tree (QR) = \(\frac{BC}{AC}\) x PR Substituting the values of PR, BC and AC in the above equation, we can get length of QR i.e., the height of the tree.

Measuring height of a tree using trigonometric ratios.This experiment can be conducted on a clear sunny day. Look at the figure given above. Height of the tree is QR, height of the stick is BC. Thrust a stick in the ground as shown in the figure. Measure its height and length of its shadow. Also measure the length of the shadow of the tree. Using these values, how will you determine the height of the tree?

Answer»

Rays of sunlight are parallel.

So, ∆PQR and ∆ABC are equiangular i.e., similar triangles.

Sides of similar triangles are proportional.

∴ \(\frac{OR}{BC}\) = \(\frac{PR}{AC}\)

∴ Height of the tree (QR) = \(\frac{BC}{AC}\) x PR

Substituting the values of PR, BC and AC in the above equation, we can get length of QR i.e., the height of the tree.