History of Science Museum

My favorite display was the quartant. In trigonometry one subject that always confused me was using ratios to find the heights of objects. To find the hight of an object with a quartant, all that is needed it the elevation of the quartant and the distance from the quartant to the tree. Then, the sites of the quartant can be set at the top of the tree. This gives us the angle created from the top of the tree to quartant against a horizontal plane. We know cosine of that angle is equal to the distance to the object, in the case of the tree. Therefore the hypotenuse can be calculated as the distance divided by the cosine of the angle. Since the hight of the tree relative to the quartant is equal to the hypotenuse times sine of the angle, the hight is equal to sine of the angle times the distance to the tree divided by cosine of the angle, which simplifies to distance times the tangent of the angle!