Question

1) Find the angle of depression of stick leaning against a wall of length 13m and the foot of the ladder is 6.5m from the wall. a) 30 b) 45 c) 60 d) 75

Answer 1

Step-by-step explanation:

correct answer is (b) 45

Answer 2

Answer:

The angle of depression is $60^{0}$.

Step-by-step explanation:

Let us construct a right-angled ΔABC with the given information.

Let AB be the wall and AC be the ladder leaning against it such that its top touches the wall at point A and foot of the ladder touches the ground at C.

It is given that the length of the ladder AC is $13m$.

It is also given that the distance of the foot of the ladder from the bottom of the wall BC is $6.5m$.

Let the angle of depression be θ.

Now, consider the ΔABC,

Hypotenuse $=13m$

Adjacent side of ∠θ $=6.5m$

$cos$θ $=\frac{adjacent}{hypotenuse}$

$cos$θ$=\frac{BC}{AC}$

$cos$θ$=\frac{6.5}{13}$

$cos$θ$=\frac{1}{2}$

$cos$θ$=cos 60^{0}$

Therefore θ$=60^{0}$

Hence we get that the angle of depression of ΔABC is $60^{0}$.