Question

A 24-foot ladder leaning against a wall makes a 30 ° angle with the ground . How high up on the building is the top of the ladder ?

HELP ASAP

Answer 1

`12\:\mathrm{ft}`

Explanation:

When the ladder is leaning against the wall, a 30-60-90 triangle is formed. The ladder acts as a 24-foot hypotenuse. Because the height is facing the
`30^(\circ)` angle, the height is half the hypotenuse (30-60-90 rules). If you forget the side rules for a 30-60-90 triangle, simply use basic trig on the right triangle:

`\sin 30^(\circ)=(h)/(24),\\h=24\sin 30^(\circ),\\h=24\cdot (1)/(2),\\h=\fbox{$12\:\mathrm{ft}$}`.