An observer of height h stands on an incline at a distance d from the base of a building of height T. the angle of elevation from the observer to the top of the building is theta and the incline makes an angle of alpha witht he horizontal. Express T, in terms of h, d, theta and alpha. H=6ft, d=50ft, alpha=15 degrees, theta =31.4 degress
please help.unable to figure this out
answer
To find the expression for T in terms of h, d, theta, and alpha, we can use trigonometry.
Considering the triangle formed by the observer, the top of the building, and the base of the building, we can use the tangent function:
tan(theta) = T / d
Rearranging the equation:
T = d * tan(theta)
Next, let's focus on the triangle formed by the observer, the point on the incline directly below the observer, and the base of the building. We can use the tangent function again:
tan(alpha) = h / d
Rearranging the equation:
h = d * tan(alpha)
Now, we can substitute the value of d from the second equation into the first equation:
T = (h / tan(alpha)) * tan(theta)
Given that h = 6 ft, d = 50 ft, alpha = 15 degrees, and theta = 31.4 degrees, we can plug in the values:
T = (6 / tan(15)) * tan(31.4)
Using a calculator to find the tangent of the angles:
T = (6 / 0.267949) * 0.631726
Calculating the result:
T ≈ 22.395 ft
Therefore, T ≈ 22.395 ft.