Question

A man standing near a building notices trhat the angle of elevation to the top of the buiilding is 64. he then walks 240 feet farther away from the building and finds the angle of elevation to the top to be 43. how tall is the building

Answer 1

To find the height of the building, we can set up and solve equations using trigonometry and the concept of similar triangles. The height can be found using the tangent function and the angles of elevation.

Step-by-step explanation:

To solve this problem, we can use trigonometry and the concept of similar triangles. Let's denote the height of the building as 'h'.

From the information given, we have two right triangles: one with angle of elevation 64 degrees and another with angle of elevation 43 degrees. The height of the building is the opposite side of these triangles.

Using the tangent function, we can set up the following equations:

tan(64) = h/x

tan(43) = h/(x+240)

Solving these equations simultaneously, we can find the value of h.

Answer 2

see the picture attached to better understand the problem
we know that
in the right triangle ABC
tan 64°=AB/AC------> AB=AC*tan 64°-----> AB=x*tan 64°---> equation 1

in the right triangle ABD
tan 43°=AB/DA----> AB=DA*tan 43°---> AB=(240+x)*tan 43°---> equation 2

equate equation 1 and equation 2
x*tan 64°-=(240+x)*tan 43°---->x*tan 64=240*tan 43+x*tan 43
x*[tan 64-tan 43]=240*tan 43-----> x=240*tan 43/[tan 64-tan 43]
x=200.22 ft

AB=x*tan 64----> AB=200.22*tan 64-----> AB=410.51 ft

the answer is
410.51 ft