Question

7. A local sign company needs to install a new billboard. The signpost is 30 m tall, and the ladder truck is parked 24 m away from the bottom of the post due to an uneven ravine. How long must the ladder be in order to reach the top of the signpost from the ladder truck?​

Answer 1

Solution :

Here ,

• Height of sign post = 30 m

• Distance between signpost and truck = 24 m

Let the

• Top of signpost = A

• Bottom of signpost = B

• The end of truck facing sign post be = C

Now as we can clearly imagine that the ladder will act as an hypotenuse to the Triangle ABC .

Where

• AB = Height of signpost = 30 m

• BC = distance between both = 24 m

• AC = Minimum length of ladder

→ AC² = AB² + BC² ( As we can see AB is perpendicular to BC )

→ AC² = (30)² + (24)²

→ AC² = 900 + 576

→ AC² = 1476

→ AC = 38.41875

or AC apx = 38.42

So minimum height of ladder = 38.42

Answer 2

This question can be solved by using the formula of "Pythagora's Theorem".

The ladder must be "38.42 m" long.

If we imagine the whole situation in terms of a right-angled triangle, we can safely assume the height of the billboard (which is the pole supporting the billboard) as the perpendicular of the right-angled triangle. The distance between the signpost and the truck can be assumed as the base of the triangle. The length of the ladder will then be acting as the Hypotenuse of the right-angled triangle.

The attached picture clearly depicts the condition explained in the above paragraph.

Now applying Pythagora's Theorem to this situation, we get:

$Hypotenuse^2 = Perpendicular^2+Base^2\\Length\ of\ Ladder^2 = (30\ m)^2+(24\ m)^2\\L^2 = 1476\ m^2$

L = 38.42 m

Learn more about Pythagora's Theorem here:

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