An easy Trigonometry problem of class-11

Geometry Level 3

Two trees A and B are on the same side of a river. From a point C in the river, the distances of trees A and B are 250 meters and 300 meters respectively. If angle C=45 degrees, find the distance between the trees (in meters, to 1 decimal place).

The answer is 215.5.

1 solution

Tom Engelsman
Mar 27, 2021

Easily solved via the Law of Cosines:

$AB^{2} = AC^{2} + BC^{2} - 2(AC)(BC) \cos \angle{ACB} = 250^2 + 300^2 - 2(250)(300) \cos(\pi/4)$ ;

or $AB = \sqrt{ 250^2 + 300^2 - 2(250)(300) \cos(\pi/4)} \approx \boxed{215.48}$ meters.

An easy Trigonometry problem of class-11

The answer is 215.5.

1 solution

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