Answer:
Height of the building ≈ 947.34 ft
Step-by-step explanation:
Jack eyes are 5 ft above the ground .He is standing 500 ft from the base of a building .His line of sight forms angle with the top of the building at 67°. The height of the building can be computed below.
The illustration forms a right angle triangle. The opposite sight of the triangle is the unknown. The height of the building can be found by using the tangential ratio.
adjacent = 400 ft
angle = 67°
tan 67° = opposite/adjacent
tan 67° = a/400
cross multiply
a = 400 tan 67°
a = 400 × 2.35585236582
a = 942.34094633
Adding 5 ft to the total height of the building will be 5 + 942.34094633 = 947.34094633
Height of the building ≈ 947.34 ft
Answer:
The height of the building is 942.34 feet
Step-by-step explanation:
Here we have that;
A right triangle is formed with vertices at the base of the building, Jack's eyes and the top of the building
The hypotenuse of the right triangle is formed by Jack's line of sight and the top of the building
The side opposite to the 67° angle is the height of the building
Since the distance from where Jack is standing to the building base = 400 ft = The adjacent side of the formed right triangle
Therefore, Tan(67) = (Height of the building)/(Jack's distance from the building)
Tan(67) = (Height of the building)/400 ft
∴ The height of the building = 400 ft × Tan(67) = 942.34 ft.
