A 30foot flagstaff is fixed in the center of a circular tower 40 feet in diameter. From a point in the same horizontal plane as the foot of the tower the angles of elevation of the top of the flagstaff and the top of the tower are found to be 36 and 30 degree respectively. Find the height of the tower.

Look at the first of the "Related Questions" below.

The poster had forgotten to give one of the angles and in Steve's solution he called it A.

In your problem we know A = 36°
so all you have to do is replace A with 36 and go for it.

You should get appr 59.86

116

To find the height of the tower, we can use trigonometry and the given angles of elevation.

Let's break down the problem step-by-step:

Step 1: Draw a diagram to represent the situation. Label the given measurements and angles.

-------
|____|
/ \
/ \
/ \
/__________\

A B C

A = Flagstaff
B = Tower
C = Point on the same horizontal plane as the foot of the tower

Step 2: In the triangle ABC, we have two angles of elevation, 36 degrees and 30 degrees. The angle at C is 90 degrees since we have a right triangle.

Step 3: We need to find the height of the tower, which is the length BC.

Step 4: Use the tangent function to find the height of the tower.

tan(30 degrees) = height of the tower (BC) / base of the tower (AB)

Step 5: Substitute the known values into the equation.

tan(30 degrees) = BC / 20 feet (since AB = 20 feet)

Step 6: Solve for BC.

BC = 20 feet * tan(30 degrees)

Step 7: Calculate the value of tan(30 degrees).

tan(30 degrees) = 1/sqrt(3) (approximately 0.5774)

Step 8: Substitute the value of tan(30 degrees) into the equation.

BC = 20 feet * 1/sqrt(3)

Step 9: Simplify the expression.

BC = 20/sqrt(3) feet

Step 10: Rationalize the denominator.

BC = (20/sqrt(3)) * (sqrt(3)/sqrt(3))

= (20*sqrt(3))/(3)

Step 11: Simplify the expression.

BC = 20*sqrt(3)/3

Therefore, the height of the tower (BC) is approximately 11.547 feet.

So, the height of the tower is approximately 11.547 feet.

To find the height of the tower, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side.

Let's assign variables as follows:
h = height of the tower
l = length of the flagstaff

From the given information, we know that:
l = 30 feet (length of the flagstaff)
d = 40 feet (diameter of the tower)

Using trigonometry, we can find the height of the tower as follows:

1. Find the length of the side opposite the 36-degree angle (length of the tower plus length of the flagstaff):
opposite side = h + l

2. Find the length of the side adjacent to the 36-degree angle (half of the diameter of the tower):
adjacent side = d/2 = 40/2 = 20 feet

3. Using tangent, we can set up the following equation:
tan(36 degrees) = opposite side / adjacent side

4. Substitute the values:
tan(36 degrees) = (h + l) / 20

5. Solve for (h + l):
(h + l) = tan(36 degrees) * 20

6. Find the length of the side opposite the 30-degree angle (height of the flagstaff):
opposite side = l = 30 feet

7. Find the length of the side adjacent to the 30-degree angle (half of the diameter of the tower):
adjacent side = d/2 = 40/2 = 20 feet

8. Using tangent, we can set up the following equation:
tan(30 degrees) = opposite side / adjacent side

9. Substitute the values:
tan(30 degrees) = 30 / 20

10. Solve for 30:
30 = tan(30 degrees) * 20

11. Solve for h:
h = (h + l) - 30

Finally, we can substitute the value of l from step 6 into step 11 to solve for h.