Question

Assertion (A): If a ladder makes an angle of 30° with the wall and its lower end is 1.5 m from the wall, then the length of the ladder is 3 m. 

Reason (R): cos 60° = `1.5/"length of ladder"`

Options

• Both A and R are true, and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

Both A and R are true, and R is the correct reason for A.

Explanation:

Ladder makes a 30° angle with the wall, so the angle with the ground is 60°.

Distance from wall (horizontal) = 1.5 m

Use right triangle trigonometry.

`cos(60°) = "adjacent(base)"/("hypotenuse"("ladder length"))`

cos(60°) = `1.5/"ladder length"`

cos(60°) = ladder length = `1.5/cos(60°)`

= `1.5/0.5`

= 3 m