Given:
Height of Mountain A = 5210 feet
Distance of Mountain A from a helicopter above the peak = 1000 feet
Angle of depression:
Mountain B to helicopter = 43 degrees
Mountain B to Mountain A = 19 degrees
First, draw an illustration and label the enumerated given values.
Observe that there are two right triangles formed:
From the triangle formed by the helicopter and Mountain B,
let x = total height of mountain B
y = leg of first triangle (helicopter and mountain b)
h = hypotenuse
Use the Pythagorean Theorem:
cos (43) = y / h
From the second triangle formed by mountain b and a,
cos (19) = (1000 + y) / h
solve for h and y
then, solve for the height of Mountain B:
x = 1000 + y + 5210
You would form this inequality:
52 + 2x < (or equal to) 180
Then, solve as you would in an ordinary equation.
Subtract 52 from both sides of the sign. 180 - 52 = 128.
So, 2x is less than or equal to 128.
Divide 128 into two to get 64.
The height of the frame must be 64 inches.
4y - 1 = 7 / + 1 ;
4y = 8 /÷4 ;
y = 2 ;
Total tax
1,000×0.02+2,000×0.04
+27,000×0.05=1,450
