Final answer:
Using trigonometric functions, the height of the dam based on the angle of elevation and given distance is not directly matching the provided options, suggesting there may be an error in the question. For the algebraic expression, multiplying 3 by each term of \( \frac{5}{4}n + 1.8 \) results in \( \frac{15}{4}n + 5.4 \), which is option b).
Step-by-step explanation:
To find the height of the dam, we can use trigonometry, specifically the tangent function, which relates the angles of a right triangle to the lengths of the sides. The formula for the tangent of the angle of elevation (\( \tan(\theta) \)) is equal to the opposite side over the adjacent side, so solving for the height (\( h \)) of the dam, we have:
\[ \tan(26\degree) = \frac{h}{90 \text{ meters}} \]
Thus, to find \( h \), multiply both sides by 90 meters:
\[ h = 90 \text{ meters} \times \tan(26\degree) \]
After calculating, the height \( h \) comes out to approximately 40.89 meters, which is not an option given. Therefore, this might be a trick question or there may be a mistake in the options provided. Now, for the product of 3 and \( \frac{5}{4}n + 1.8 \), distribute the 3:
\[ 3 \left( \frac{5}{4}n + 1.8 \right) \]
Multiplying each term by 3 gives us:
\[ \frac{15}{4}n + 5.4 \]
This corresponds to option b), which is \( \frac{15}{4}n + 5.4 \).