Question

To safely position a ladder against a house,the angle of elevation should be 76•if you put a 25 foot ladder against your house,how far away from the house will the base of the ladder be?

Answer 1

Answer: The base of the ladder would be 6 ft away from the house.

Step-by-step explanation: Please refer to the diagram attached for details.

The ladder is represented by line HB and the length of the ladder is given as 25 ft. Also to be safely placed against the wall, the ladder should be placed at an angle of elevation of 76 degrees, hence angle B is labeled 76. The wall of the house itself is line HG. The base of the wall is point G, so the distance from the house to the base of the ladder would be line GB (labeled as ‘h’). Having identified two sides (one side is yet unknown) and a reference angle, we can use trigonometric ratios.

With the adjacent (side between the right angle and the reference angle) and the hypotenuse (side facing the right angle), we can now use the Cosine ratio;

CosB = adjacent/hypotenuse

Cos76 = h/25

By cross multiplication we now have Cos76 x 25 = h

0.2419 x 25 = h

h = 6.0475

Approximately h, equals 6.

Therefore the base of the ladder would be 6 ft away from the house