a 18 foot ladder is placed against a building so the angle between the ground and the ladder is 82 degrees. how high does the ladder reach on the building?
After reviewing the basic trig ratios of right-angled triangles, you will see that
height/18 = sin82°
height = 18sin82° = ...
Draw a diagram and review your basic trig functions. It should be clear that the height h can be found using
h/18 = sin82°
To find out how high the ladder reaches on the building, you can use trigonometry. In this case, you can use the sine function to calculate the height.
The sine of an angle (82 degrees in this case) is equal to the opposite side length (the height the ladder reaches) divided by the hypotenuse (the length of the ladder).
Using the formula: sin(angle) = opposite/hypotenuse
Let's plug in the given values:
sin(82 degrees) = h/18 feet
Now, we can rearrange the equation to solve for h (the height):
h = sin(82 degrees) * 18 feet
To calculate this, you can use a scientific calculator or the trigonometric functions in a programming language. The output will give you the height of the ladder on the building.