When the angle of eleviation of a sun is 30 degree. The shadow of a vertical tower is 20m longer than when the angle of eleviation of a sun is 60 degree. Find the of the tower.
It would help if you proofread your questions before you posted them, i.e., "Find the of the tower".
To solve this problem, we can use the concept of trigonometry. Let's break down the given information:
When the angle of elevation of the sun is 30 degrees, the length of the shadow of the tower is unknown.
When the angle of elevation of the sun is 60 degrees, the length of the shadow of the tower is 20m longer than the previous case.
Let's assume the height of the tower is "h" meters and the length of the shadow when the angle of elevation is 30 degrees is "x" meters.
Using trigonometry, we can write the following equations:
Equation 1: tan(30°) = h / x
Equation 2: tan(60°) = h / (x + 20)
Now, let's solve these equations step by step:
Equation 1: tan(30°) = h / x
tan(30°) = 1 / √3 (simplified value of tan(30°))
√3 / 3 = h / x (cross-multiplication)
x = 3h / √3 (equation 3)
Equation 2: tan(60°) = h / (x + 20)
√3 = h / (x + 20) (simplified value of tan(60°))
h = √3(x + 20) (cross-multiplication)
Now, substitute equation 3 into equation 4:
h = √3((3h / √3) + 20) (substituting x from equation 3)
h = 3h + 20√3 (simplifying the equation by canceling out the √3 terms)
Next, move the 3h term to the left side of the equation:
h - 3h = 20√3
-2h = 20√3
Finally, solve for h by dividing both sides by -2:
h = 20√3 / -2
h = -10√3
Since the height cannot be negative, we disregard the negative value. Therefore, the height of the tower is 10√3 meters.