SOLUTION: The Leaning Tower of Pisa is 179 ft.high, making a 5.1 degree angle with vertical find b?

Question 556833: The Leaning Tower of Pisa is 179 ft.high, making a 5.1 degree angle with vertical find b?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
height of the leaning tower of pisa is 179 feet
it makes a 5.1 degrees from the vertical.
it's angle to the ground would be 90 - 5.1 = 84.9 degrees.
the height of the vertical would be one leg of a right triangle.
to find the vertical height of the tower, we would take the sine of 84.9 using the formula:
sine (84.9) = opposite divided by hypotenuse.
opposite i x
hypotenuse is 179
formula becomes:
sine (84.9) = x/179
multiply both sides of this equation by 179 to get:
x = 179 * sine (84.9)
this results in:
x = 178.2913507 feet
that's the vertical height.
if you worked it the other way, it would be using cosine (5.1).
since cosine (5.1) equals sine (84.9) you would get the same answer.
179 * cosine (5.1) = 178.2913507
the diagram of what i mean is shown below:
$$$$

AB is the leaning tower of pisa.
AC and DB are the vertical heights (they are equal to each other in length).
angle ABD is the 5.1 degree angle that the leaning tower of pisa makes with the vertical.
ABC is the 84. degree angle that the leaning tower of pisa makes with the horizontal which is the ground.
if you measure x using triangle ABC, then you would take the sine of 84.9 degrees.
if you measure x using triangle ABD, then you would take the cosine of 5.1.
ABC and ABD are both right triangles.
the leaning tower of pisa is the hypotenuse of both these triangles.

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