Question

This problem is completing our example from the end of the recording today.) We have a 20 foot ladder and lean it against the house at a 75 degree angle with the ground. a) How far up the house does the ladder reach? b) How far from the house is the bottom of the ladder?

Answer 1

a) The ladder reach 19.32 foot up the house

b) The bottom of the ladder is 5.18 foot from the house

Explanation:

An illustrative diagram of the scenario is attached below.

From the diagram, we have a right angle triangle with the length of the ladder being the hypotenuse. The opposite indicates how far up the house the ladder reach and the adjacent indicates the distance of the bottom of ladder from the house.

a) To determine how far up the house the ladder reach, that is the opposite. Let the opposite be y

From the formula

Sinθ = Opposite / Hypotenuse

Where θ is the angle subtended

Here θ = 75°

Hypotenuse = 20 foot

∴ sin75° = y / 20

y = 20 × sin75°

y = 20 × 0.9659

y = 19.32 foot

Hence, the ladder reach 19.32 foot up the house.

b) To determine how far from the house the bottom of the ladder is, that is the adjacent. Let the adjacent be x

From the formula

Cosθ = Adjacent / Hypotenuse

Where θ is the angle subtended

Then,

cos75° = x / 20

∴ x = 20 × cos75°

x = 20 × 0.2588

x = 5.18 foot

Hence, the bottom of the ladder is 5.18 foot from the house.