the angle of elevation from point on the ground to the top of a pyramid is 20 degrees 20 degrees the angle elevation from a point 189 feet farther back to the top of the pyramid is 10 degrees 20 degrees. find the height of the pyramid
tan20o = Y/X1
Y = X1*tan20.
tan10o = Y/(X1+X2).
Y = (X1+X2)*tan10
X1*tan20 = (X1+X2)*tan10
X2 = 189 Ft.
X1*tan20 = (X1+189)*tan10
X1*tan20 = X1*tan10+189*tan10
X1*tan20-X1*tan10 = 189*tan10
0.364X1-0.176X1 = 33.33
0.188X1 = 33.33
X1 = 177.3 Ft.
Y = h = X1*tan20 = 177.3*tan20=64.5 Ft.
NOTE: 2 rt. triangles were formed with a common vert. side and a shared hor. side(X1 and X2).
To find the height of the pyramid, we can use trigonometric ratios.
Let's assume that the height of the pyramid is "h" and the distance from the point on the ground to the pyramid is "x". We need to find the value of "h".
From the given information, we have two right-angled triangles.
In the first triangle, the angle of elevation is 20 degrees, and the opposite side is "h" (the height of the pyramid), while the adjacent side is "x" (the distance from the point on the ground to the pyramid).
In the second triangle, the angle of elevation is 10 degrees, and the opposite side is "h" (the height of the pyramid), while the adjacent side is "x + 189" (the distance from the point 189 feet farther back to the pyramid).
Using the tangent function for both triangles, we can set up the following equations:
1. tan(20) = h / x
2. tan(10) = h / (x + 189)
We can rearrange the equations to solve for "h".
1. tan(20) * x = h
2. tan(10) * (x + 189) = h
Now we can set the two expressions for "h" equal to each other:
tan(20) * x = tan(10) * (x + 189)
Now we can solve for "x":
x = (tan(10) * 189) / (tan(20) - tan(10))
Using this value of "x", we can substitute it back into either of the original equations to find the height "h" of the pyramid.
For example, we can use equation 1:
h = tan(20) * x
Now we can substitute the value of "x" to find the height "h".
Note: Remember to convert the angle values to radians if using a calculator that works with radians.