the angles of elevation of a tower at two places due west of it are 63 degrees and 56 degrees. given that the foot of the tower and the two points are on ground level and the distance between the two points is 20 meters, find the height of the tower.
You have to draw a picture to see what's going on. Once you draw the picture, you see there are 2 right triangles.
tan 56 = x/(20 + y) where y is the distance between the foot of the tower and the first point, and x is height of tower.
and tan 63 = x/y.
Now you have 2 equations and 2 unkowns, so you can solve it.
Repost if you need more help.
thanks!
you're welcome
To find the height of the tower, we can set up two equations using the tangent function:
From the first triangle, we have tan(56) = x / (20 + y), where x is the height of the tower and y is the distance between the foot of the tower and the first point.
From the second triangle, we have tan(63) = x / y.
We now have two equations and two unknowns, x and y. We can solve these equations simultaneously to find the values of x and y.
First, rearrange the equations to isolate x:
In the first equation, multiply both sides by (20 + y):
tan(56) = x / (20 + y)
x = (20 + y) * tan(56)
In the second equation, multiply both sides by y:
tan(63) = x / y
x = y * tan(63)
Now that we have two expressions for x, we can set them equal to each other:
(20 + y) * tan(56) = y * tan(63)
Next, distribute and combine like terms:
20 * tan(56) + y * tan(56) = y * tan(63)
Now, isolate y by subtracting y * tan(63) from both sides:
20 * tan(56) = y * tan(63) - y * tan(56)
Factor out y on the right side:
20 * tan(56) = y * (tan(63) - tan(56))
Finally, divide both sides by (tan(63) - tan(56)):
y = (20 * tan(56)) / (tan(63) - tan(56))
Now substitute this value of y into either of the original equations to solve for x:
x = y * tan(63)
x = [(20 * tan(56)) / (tan(63) - tan(56))] * tan(63)
Simplify and evaluate the expression to find the value of x, which represents the height of the tower.