Trigonometry problem

Question

The proper angle for a ladder is about 75 degrees. Suppose you have a 13 ft ladder. How high can it reach.

Answer 1

Given: The proper angle for a ladder is 75 degrees.

Suppose you have a 13 foot ladder.

Find: How high can your ladder reach?

SOLUTION:

Visualize/Sketch a 75-degree angle in the first quadrant.

Visualize/Sketch a vertical line to make a right-triangle with the 75-degree angle inside.

The diagonal line of the triangle represents your ladder. It's the hypotenuse.

Sin(75) = (height) / (hypotenuse)

Sin(75) = (height) / (13)

height = 13 * Sin(75)

height = 12.557 feet

Answer 2

\

| \

| \

| \ Length of ladder leaning against the wall is 13 ft.

| \

| \

|____\ Angle of base = 75° = Θ and vertical height of the ladder is X ft.

Then Sin(θ) = X/13 X = 13xSin(75) = 12.56 feet in height.