"Published in Newark, California, USA"
Show that in any prism the area of a right section is equal to the product of the base and the sine of the angle between a lateral edge and the base. (This relation is used in connection with the reflection of light through prisms.)
Solution:
To illustrate the problem, it is better to draw the figure as follows
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| Photo by Math Principles in Everyday Life |
If the area of a base and the altitude are given, then the volume of a prism is
If the area of a right section and the length of a lateral edge or slant height are given, then the volume of a prism is
Equate the two equations above, we have
Consider a right triangle from the figure above,
Substitute the value of h to the above equation, we have
Therefore,
