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A ladder leaning against a wall makes an angle θ with the horizontal ground such that tan θ = 158\frac{15}8815​ If the height of the top of the ladder
Question

A ladder leaning against a wall makes an angle θ with the horizontal ground such that tan θ = 158\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.​

A.

18

B.

16

C.

14

D.

20

Correct option is B

Given:

tanθ=158\tan \theta = \frac{15}{8}​​

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

Formula Used:

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

Solution: 

Given tanθ=158\tan \theta = \frac{15}{8}​ and height = 30 m, we can write:

158=30distance from the wall\frac{15}{8} = \frac{30}{\text{distance from the wall}}​​

Let the distance from the wall be x. Then:

158=30x\frac{15}{8} = \frac{30}{x}​​

15x=8×3015x = 8 \times 30​​

15x = 240

x = 24015=16 m\frac{240}{15} = 16 \text{ m}​​

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

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