We are given that two office buildings are $51$ meters apart and that the height of the taller building is $207$ meters. We also know that the angle of depression from the top of the taller building to the top of the shorter one is $1 5^{\circ},$ and we want to evaluate the height of the shorter building. Let's sketch a diagram of this situation.

Notice that a diagram makes the problem much clearer. Since we are asked to find the height of the shorter building, we should find the difference between these buildings and subtract it from $207 .$ Let's call this difference $d .$

Next let's recall that the angle of depression and corresponding angle of elevation are congruent. Therefore, the angle of elevation from the top of the shorter building to the top of the taller building is also $1 5^{\circ} .$

To find the value of

d,

we can use one of the trigonometric ratios. Let's recall that the tangent of an angle is the ratio of the side opposite this angle to the side adjacent to this angle. Using this definition, we can write an equation for

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