At a certain point in a large level park, the angle of elevation to the top of an office building is 30 degrees. If you move 400 ft closer to the building, the angle of elevation is 45 degrees. To the nearest 10 feet, how tall is the building?
Please make it as simple as possible, thanks.
+14995 Hello Guest!
At a certain point in a large level park, the angle of elevation to the top of an office building is 30 degrees. If you move 400 ft closer to the building, the angle of elevation is 45 degrees. To the nearest 10 feet, how tall is the building?
Please make it as simple as possible, thanks.
An einem bestimmten Punkt in einem großen ebenen Park. Der Höhenwinkel nach oben zu einem Bürogebäude beträgt 30 Grad. Wenn Sie sich 400 ft näher an das Gebäude bewegen, ist der Höhenwinkel 45 Grad. Um 10 ft genau, wie hoch ist das Gebäude?
The law of sines
triangle ABC. c = 400ft α = 30° β = 135° γ = 15°
a / sin α = c / sin γ
a = c * sin α / sin γ = 400ft * sin 30° / sin 15° = 772,74066ft
Triangle (90 ° 45 ° 45 ° / a h h)
2h² = a²
h = √(a² / 2) = √(772.74066² / 2) = 546.410161512ft
h = 546.41ft
The building is 546.41ft high.
Greeting asinus :- )
!
+37146 At 45 degrees both legs of the triangle are equal, i.e. the distance FROM the building and the HEIGHT of the building are EQUAL. (T)
At 30 degrees then Tan(30) = T/(400+T)
.57735 = T/(400+T) Solve for T
T= 546.40 ft tall
