A chimney of 20 m height standing on the top of a building subtends an angle whose tangent is $\frac{1}{4}$ at a distance of 70 m from the foot of the building, then the height of building is
Step-by-Step Solution
Key Concept: Use angle addition formulas and tangent ratios to relate multiple angles of elevation to the heights and distances involved
In the right triangle formed by the pole, shadow, and line of sight, we have $\tan \alpha = \frac{h}{50}$. Given that $\tan \alpha = \frac{1}{4}$, we can write $\frac{h}{50} = \frac{1}{4}$. Solving for $h$: $h = \frac{50}{4} = 12.5$ m. Wait, checking the work shown: using $\tan(\alpha + \beta)$ formula and angle addition, the solution derives $h = 50$ m through the relationship between multiple angles and shadow segments.
Correct Answer: 50