how high does the ladder reach up the side of the building

Question

A 32-ft ladder leans against a building so that the angle between the ground and the ladder is 70°. How high does the ladder reach up the side of the building? (Round your answer to four decimal places.)

Answer 1

Ladder top

| \

| \

| \

| \

| \ L

h | \

| theta ( \

---------Ladder bottom

Here we have a visual representation of the ladder. It forms a right triangle by leaning against the wall. The length of the ladder, L, is the hypotenuse which is 32 feet. The angle near the ladder bottom is 70 degrees. We want to find h, which is the side opposite of the angle. Using trigonometry:

opposite / hypotenuse = sin theta

in variables, written as:

h / L = sin theta

Solving for h:

h = L * sin theta

Plugging in:

h = 32 feet * sin 70 degrees = 32 feet * 0.939693 = 30.07 feet

Answer 2

sin = opp/hyp

sin 70 = h/32

.93969 = h/32

30.0702 feet = h