Trigonometry Grade 11

Question

points p and q lie 240 m apart in line with and on opposite sides of a communications tower. the angles of elevation to the top of the tower from p and q are 50° and 45°, respectively. determine the height of the tower.

given the answer 130.5 , show all steps of how to get the answer given.

Answer 1

Draw and label a diagram!

b represents the point at the base of the tower

h represents the height of the tower

h = bq (Can you say why?)

bp = 240 - bq

h / bq = tan 45° → h = bq tan 45°

h / (240 - bp) = tan 50° → h = (240 - bp) tan 50º

bq tan 45º = (240 - bq) tan 50º

Can you solve for bq and answer?