A ladder leaning against a wall makes an angle θ with the horizontal ground such that tan θ = $$\frac{15}8$$ If the height of the top of the ladder from the wall is 30 m, find the distance (in m) of the foot of the ladder from the wall.​

Correct option is B

Given:

​$$\tan \theta = \frac{15}{8}$$​​

Height of the top of the ladder from the wall = 30 m

Formula Used:

​$$\tan \theta = \frac{\text{height of the ladder}}{\text{distance from the wall}}$$​​

Solution: ​

Given $$\tan \theta = \frac{15}{8}$$​ and height = 30 m, we can write:

$$\frac{15}{8} = \frac{30}{\text{distance from the wall}}$$​​

Let the distance from the wall be x. Then:

$$\frac{15}{8} = \frac{30}{x}$$​​

​$$15x = 8 \times 30$$​​

15x = 240

x = $$\frac{240}{15} = 16 \text{ m}$$​​

Thus, the distance of the foot of the ladder from the wall is 16 m.