Problems involving Geometry (Pythagorean Theorem)

Question

How long is the ladder which makes an angle of 30° with the side of the house and whose foot is 104 cm away from the base of the house? Show your solution.

Answer 1

We can use the law of sin to solve for the missing side of your triangle.

We know from SOHCAHTOA that we use sin to evaluate when we have an angle, an opposite, and a hypotenuse. The formulation is:

1. sin(30) = Opposite / Hypotenuse = 104 / x

Solving for x:

1. x = 104 / sin (30) = 104 / (1/2) = 2* 104 = 208 cm

Answer 2

A 30-60-90 triangle is one of the "special" right triangle and always has the following relationships between the sides:

The side opposite the 30° angle is the shortest so, call it "s". The hypotenuse then is "2s" and the other leg is s√3.

So, in this case "s" is 104 cm. Therefore the hypotenuse (or length of the ladder) is 2(104) or 208 cm.