A 4 meter long ladder leans against a 90 degree wall at a 68 degree angle.
How far is the top of the ladder from the ground?
How far is the bottom of the ladder from the wall?

Answer:

Step-by-step explanation:

We use trig to answer these questions:

sin x = opposite side of a triangle / hypotenuse

cos x = adjacent side / hypotenuse

Construct a right triangle with hypotenuse 4 m and lower angle 68 degrees.

The height of the top of the ladder  is then defined by:

sin 68 degrees = height / 4 m, which yields (4 m)(sin 68) = height =

3.71 m

and the distance of the bottom of the ladder from the wall as follows:

cos 68 degrees = horizontal distance / hypotenuse =

1.50 m

The top of the ladder is 3.7088 m away from the ground.

The bottom of the ladder is 1.5 m away from the wall.

According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Given:

Angle = 68 degree

Hypotenuse = 4 m

Now, using Trigonometry

sin 68 = P/ H

0.9272 = P/ 4

P = 3.7088 m

Thus, the top of the ladder is 3.7088 m away from the ground.

Now, using Pythagoras theorem

H²= P² + B²

4² = (3.7088)² + B²

16 = 13.75 + B²

B² = 2.25

B= 1.5 m

Thus, the bottom of the ladder is 1.5 m away from the wall.

Learn more about Pythagoras theorem here:

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