Question

From the figure, \(θ=\)

• A. 45°
• B. 60°
• C. 30°
• D. 75°

Answer 1

The Correct Option is B

To solve the problem, we need to determine the value of \(\theta\) in the given right triangle \( \triangle ABC \), where \( AB = 100 \, \text{m} \) and \( BC = 100\sqrt{3} \, \text{m} \).

1. Understanding the Right Triangle:
The triangle \( \triangle ABC \) is a right triangle with \( \angle B = 90^\circ \). The side opposite to \(\theta\) is \( BC \), and the side adjacent to \(\theta\) is \( AB \). We are tasked with finding \(\theta\).

2. Using Trigonometric Ratios:
The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side: \[ \tan \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{BC}{AB} \] Substituting the given values: \[ \tan \theta = \frac{100\sqrt{3}}{100} = \sqrt{3} \]

3. Identifying the Angle:
We know from trigonometric values that: \[ \tan 60^\circ = \sqrt{3} \] Thus, \(\theta = 60^\circ\).

Final Answer:
The value of \(\theta\) is \({60^\circ}\).