My problem involves right-triangle trigonometry.
A man on a 135-ft vertical cliff looks down at an angle of 16 degrees and sees his friend. How far away is the man from his friend? How far is the friend from the base of the cliff?
Does the 16 degrees go to the left of the right angle or below it?
the scale on a drawing is 1/8"=1 foot.A horizontal line measuring 3-5/16"on the drawing would represent a length of(answer)feet.
To solve this problem, we will use right-triangle trigonometry.
First, let's label the given information. The vertical cliff has a height of 135 ft. The angle the man is looking down at is 16 degrees.
The 16 degrees angle should be placed below the right angle. This is because the angle is defined in relation to the vertical direction (the height of the cliff), which is perpendicular to the base of the cliff.
Now, we can use the trigonometric ratios to find the distances. In this case, we will use the tangent ratio.
The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.
Let's call the distance between the man and his friend "x". The opposite side to the angle of 16 degrees will be the height of the cliff, which is 135 ft. The adjacent side is the distance from the friend to the base of the cliff, which we will call "y".
Using the tangent ratio:
tan(16 degrees) = opposite/adjacent
tan(16 degrees) = 135/y
To find "x", we can use the same tangent ratio:
tan(16 degrees) = opposite/adjacent
tan(16 degrees) = 135/x
To solve for "x", we rearrange the equation:
x = 135/tan(16 degrees)
To solve for "y", we rearrange the equation:
y = 135/tan(16 degrees)
Now we can calculate both distances by substituting the given angle into the equations:
x = 135/tan(16 degrees)
y = 135/tan(16 degrees)