Help with math word problem?Hobbyists often compete for their model rockets to determine which rocket flies the highest. On one test launch, a rock was fired vertically upward. The angle of...

Help with math word problem?

Hobbyists often compete for their model rockets to determine which rocket flies the highest. On one test launch, a rock was fired vertically upward. The angle of elevation to the top of the flight was measure from two points 25m apart, on the same side of the launch site. The angles measure at the two points were 70 and 35. How high did the rocket fly?

neela | High School Teacher | (Level 3) Valedictorian

Posted on

We represent geometrically the figure as below:

Let T be the top of the flight (rocket). Let G be the feet of the perpendicular from T to the ground. B and A be the points on the same line and side of G.

Given angle GBT = 70 deg, angle GAT = 35 degree and AB = 25 m.TWe have to find the height GT.

We know that GT/AG= tan GAT = tan 35.

Or GT = AG*tan 35.

Or GT = (AB+BG) tan 35......(1).

GT = (25+BG) tan35, as AB = 25 m by data.

GT/BG = tan GBT = tan 70.

BG = GT/tan 70....................(2).

From (2), we substitute  GB = (GT/tan70) in (1) and we get:

GT = (25+GT/tan 70) tan 35

GT - GT tan 35/tan 70 = 25 tan 35.

GT{1- (tan 35)/tan 70} = 25 tan 35.

GT = 25tan 35/{1- tan35/tan 70}.

GT = 25 tan 35/{1-( tan 35)/tan70}.

GT = 23.4923 meter.

Therefore the height of top of the flight = 23.4923 m.