A flagstaff of placed at one corner of a rectangular playground 40m long and 30m wide. If the angle of elevation of the top of flag staff from the opposite corner of 30°, find height of the flagstaff.
(The question is complete and I have cross checked the question. )
I made a slanted ground so that I can make the flagstaff's height be clear. But this way I only see one triangle being formedd in the figure. I also drew a diagonal for the rectangle. Since rectangle is slanted so I took the angle of elevation from the opposite corner from the diagonal ( not from the ground's length)
Now I can't solve it. I am sure I have made a wrong figure.
Someone please help me how to draw the figure and how to solve.
Am i dead?
Maths teacher
To draw the figure and solve the problem, follow these steps:
Step 1: Draw a rectangle with dimensions 40m long and 30m wide. Label the opposite corners of the rectangle as A and C, and the other two corners as B and D.
Step 2: Draw a diagonal line connecting corners A and C. Label this diagonal as AC. This diagonal divides the rectangle into two congruent right triangles, ABC and ACD.
Step 3: At point C, draw a vertical line representing the flagstaff. Label the top of the flagstaff as F.
Step 4: From point B, draw a line representing the line of sight to the top of the flagstaff F.
Step 5: The given angle of elevation, 30 degrees, is the angle between the line of sight BF and the ground BC.
Now let's solve the problem:
Step 1: We have a right triangle ABC, where side AB is 30m and side BC is 40m.
Step 2: We need to find the height of the flagstaff CF.
Step 3: From triangle ABC, we can use the trigonometric ratio tangent (tan) to find the height CF.
The tangent of angle ACB (which is the angle of elevation) is equal to the opposite side (CF) divided by the adjacent side (BC).
So, we have:
tan(ACB) = CF / BC
Given that the angle of elevation ACB is 30 degrees, and BC is 40m:
tan(30) = CF / 40
Now we need to find CF:
CF = tan(30) * 40
Using a calculator, calculate the tangent of 30 degrees, which is approximately 0.5774:
CF = 0.5774 * 40
CF ≈ 23.096m
Therefore, the height of the flagstaff is approximately 23.096 meters.
If the sides are 30 and 40, the diagonal is 50
so, if the height is h,
h/50 = tan30°