Question

Simple trigonometry tells us that the tangent of an angle (abbreviated "tan 0') is equal to the length of the side opposite the angle divided by the length of the side adjacent to the angle.Your goal in this part is to translate the previous sentence into a simple, one-line formula, using symbols in place of words. In the above sentence, phrases in italics refer to quantities represented by the alphabetical letters h or l, defined in Figure 2.1; other phrases might translate to an equal sign or an arithmetic operation, such as addition, subtraction, multiplication, or diyision, as appropriate. Your completed formula relates the Sun's altitude 0 to the gnomoris height h and the shadow length l.

Answer 1

The given sentence translated into simple, one-line formula, using symbols in place of words is

sinθ = h/l

Trigonometry

From the question, we are to translate the given sentence into simple, one-line formula, using symbols in place of words

The given statement is

"the tangent of an angle (abbreviated "tan 0') is equal to the length of the side opposite the angle divided by the length of the side adjacent to the angle"

In the given diagram,

The angle is θ

The side opposite the angle is gnomon (height h)

The adjacent side is the shadow (length l)

Thus,

From the given statement, we can write that

sinθ = h/l

Hence, the given sentence translated into simple, one-line formula, using symbols in place of words is

sinθ = h/l

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