A 20 m long ladder touches the wall at a height of 10 m. The angle which the ladder makes with the horizontal isa)450b)300c)900d)600Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Answer

Use sin theta = opp / hypotenuse (opp =hight of wall , hypo = length of ladder )

sin theta = 10/20

sin theta =1/2

theta = 30 ( sin 30 = 1/2 )

so correct option is B

Answer

Given:
- Length of ladder = 20 m
- Height at which ladder touches the wall = 10 m

To Find:
- The angle which the ladder makes with the horizontal

Solution:
Let's assume the ladder as the hypotenuse of a right-angled triangle, with the wall as the vertical side and the ground as the horizontal side. The angle that the ladder makes with the horizontal is the angle opposite to the vertical side.

Step 1:
Let's label the sides of the triangle:
- Hypotenuse (ladder) = 20 m
- Vertical side (height) = 10 m
- Horizontal side (ground) = ?

Step 2:
We can use the Pythagorean theorem to find the length of the horizontal side (ground):
(horizontal side)^2 + (vertical side)^2 = (ladder)^2
(horizontal side)^2 + (10 m)^2 = (20 m)^2
(horizontal side)^2 + 100 m^2 = 400 m^2
(horizontal side)^2 = 400 m^2 - 100 m^2
(horizontal side)^2 = 300 m^2
(horizontal side) = √300 m
(horizontal side) ≈ 17.32 m

Step 3:
Now that we know the lengths of the vertical and horizontal sides, we can use trigonometry to find the angle.
The tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side.
tan(angle) = (vertical side) / (horizontal side)
tan(angle) = 10 m / 17.32 m
tan(angle) ≈ 0.577

Step 4:
To find the angle, we need to take the inverse tangent (arctan) of the ratio.
angle = arctan(0.577)
angle ≈ 30°

Conclusion:
Therefore, the angle that the ladder makes with the horizontal is approximately 30°, which corresponds to option B) 30°.

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