Question

a 12-ft ladder leans against a building so that the angle between the ground and the ladder is 74°. how high does the ladder reach on the building? (round your answer to the nearest foot.)

Answer 1

12 feet

Explanation:

Sometimes, a simple drawing is a great way to start! In the attached drawing, the red line represents the ladder, the brown represents the ground, and the black represents the building!

We want to find the side of the triangle from where the ladder meets the building to where the building meets the ground. This can be found using trigonometric identities, namely sine:

`sin\theta=(opposite)/(hypotenuse)`

Plug in known values:

`sin(74^o)=(x)/(12)`

Rearrange to isolate the variable:

`x=12sin(74^o)`

Simplify!

`x=11.535140... ft`

Round to the nearest foot:

`x=12ft`