SOLUTION: A man standing on the roof of a building 65.0 feet high looks down to the building next door. He finds the angle of depression to the roof of that building from the roof of his bui

Algebra ->  Test -> SOLUTION: A man standing on the roof of a building 65.0 feet high looks down to the building next door. He finds the angle of depression to the roof of that building from the roof of his bui      Log On


   

Question 1145813: A man standing on the roof of a building 65.0 feet high looks down to the building next door. He finds the angle of depression to the roof of that building from the roof of his building to be 34.6°, while the angle of depression from the roof of his building to the bottom of the building next door is 63.2°.
How tall is the building next door? (Round your answer to the nearest tenth.)
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
see my diagram below:

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the angle of depression from the roof of building B1 to the roof of building B2 is angle DAB which is 34.6 degrees.

the angle of depression from the roof of building B1 to the foot of building B2 is angle DAF which is 63.2 degrees.

angle EAF is equal to 90 degrees - 63.2 degrees which is equal to 26.8 degrees.

line AE is perpendicular to lines AD and CB and EF and is parallel to line DF which is also perpendicular to lines AD and CB and EF.

the height of building B1 is equal to 65 feet which is the length of line AE and also the length of line DF.

the height of building B2 is the length of line BF.

x represents the length of lines EF and CB and AD.

y represents the length of lines AC and DB.

z represents the length of lines CE and BF.

in triangle AEF, tan(26.8) = x / 65.
solve for x to get x = 65 * tan(26.8) = 32.83386263

in triangle ADB, tan(34.6) = y / x
solve for y to get y = 32.83386265 * tan(34.6) = 22.65056463

z = 65 - y = 65 - 22.65056463 = 42.34943537

that's the height of building B2.

round to the nearest tenth and the height of building B2 is 42.3 feet.

that's what i get.