The problem involves finding the height of a building using trigonometry. Let’s break it down step by step:

1. Given Information:

   • The angle of elevation: $30^\circ$
   • The distance from Salem to the base of the building (adjacent side): $50 \, \text{m}$
   • We need to find the height of the building ($x$).

2. Trigonometric Relationship: From the image, it is clear that the problem involves a right triangle where:

   • The height of the building ($x$) is the opposite side.
   • The distance from Salem to the base of the building ($50 \, \text{m}$) is the adjacent side.
   • The tangent function is defined as: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ So, in this case: $\tan(30^\circ) = \frac{x}{50}$

3. Solve for $x$: Multiply both sides of the equation by $50$: $x = 50 \cdot \tan(30^\circ)$

4. Substitute the Value of $\tan(30^\circ)$: From trigonometric tables: $\tan(30^\circ) = \frac{\sqrt{3}}{3} \approx 0.577$ Substituting this value: $x = 50 \cdot 0.577 = 28.85 \, \text{m}$

Correct Answer:

The height of the building is approximately 28.85 meters.

Dropdown Selection:

From the options visible in the image, the correct expression to choose is: $x = 50 \tan 30^\circ$

Do you have any questions or need further clarifications?

Related Questions:

1. What is the value of $\tan(45^\circ)$, and how does it apply in similar problems?
2. How would the solution change if the angle of elevation was $45^\circ$?
3. How can we verify the answer using the sine rule instead of tangent?
4. Why is $\tan(\theta)$ preferred here instead of $\sin(\theta)$ or $\cos(\theta)$?
5. What is the general relationship between the angle of elevation and the height of the building as distance changes?

Tip:

Always check if the correct trigonometric function (sine, cosine, or tangent) applies based on the given sides of the triangle!