Rani used a wooden ladder to go up on the terrace of that house she took a measuring tape to measure distance between foot of ladder from the wall horizontally and found out it 5 M where as her father told her that the terrace of the house is exactly 5 above the ground.
i)what is the angle made by the ladder with the ground
ii)angle made by ladder with wall. iii)length if ladder.
iv)tan theta in terms of sec and sin theta.
v)if foot of ladder is pulled away from the wall what will happen to the length of the ladder
Answers
Answer:
ii)angle made by ladder with wall. iii)length if ladder. iv)tan theta in terms of sec and sin theta. v)if foot of ladder is pulled away.
Given: Height of the terrace from the ground = 5m
Distance of the foot of the ladder from the wall = 5m
To find: i) angle made by the ladder with the ground
ii) angle made by the ladder with wall
iii) length of the ladder
iv) tan theta in terms of sec and sin theta
v) If the foot of the ladder is pulled away from the wall, what will
happen to the length of the ladder?
Solution: We can see that the ladder forms a right angled triangle with the wall and the ground.
Now since the sides of the triangle (height of the wall and distance of the foot of the ladder from the wall) have the same length, it is clear that the triangle formed is an isoceles one.
We know, the angles of an isoceles right angled triangle are 90°, 45° and 45°.
Therefore,
i) The angle made by the ladder with the ground = 45°
ii) The angle made by the ladder with the wall = 45°
iii) Let the length of the ladder be x cm.
Using Pythagoras' Theorem,
x² = (height of the wall)² + (distance of the foot of the ladder from the wall)²
⇒ x² = 5² + 5²
⇒ x² = 50
⇒ x = 5√2
Hence, the length of the ladder = 5√2 cm.
iv) tanθ = sinθ/cosθ
⇒ tanθ = sinθ × secθ
v) If the foot of the ladder is pulled away from the wall, the length of the ladder will decrease.