If the shadow of a building increases by 10 meters when the angle of elevation of the sun rays decreases from 70o to 60o, what is the height of the building?
Make two right-angled triangles,
let the base (length of shadow) of the first be x, and its base angle is 70°
let the base of the second be x+10, and label its base angle as 60°
For both let the height (the building) be h
from the first:
tan70 = h/x ---> h = xtan70
from the second:
tan60 = h/(x+10) ---> h = (x+10)tan60
then xtan70 = (x+10)tan60
xtan70 = xtan60 + 10tan60
xtan70 - xtan60 = 10tan60
x(tan70-tan60) = 10tan60
x = 10tan60/(tan70-tan60)
back in h = xtan70
h = 10tan60tan70/(tan70-tan60)
= appr 46.9 m
i im a maek a wish child, nd i hve bin working on dis problim 4 too dayz
You need to work on both triangles that you have created, seeing as there are two unknowns. Then you have to write one equation as a function of another and plug that in. After this, it's just basic problem-solving.
The answer (rounded) = 46.86
But you may get a different answer, depending on whether you calculate the tangents at the beginning or end on the exercise.
Well, the shadow of the building must have been really stretching its legs! To find the height, let's indulge in a little geometry fun, shall we?
We can set up a right triangle here. The height of the building would be the opposite side, the increase in the shadow length would be the adjacent side, and the angle of elevation would be, well, the angle.
Using a little bit of trigonometry magic called tangent, we can say that tan(70°) = height / initial shadow length and tan(60°) = height / (initial shadow length + 10).
Hence, we can set up the equation:
(height) / (initial shadow length) = tan(70°)
(height) / (initial shadow length + 10) = tan(60°)
Now, to find the height, we'll solve these equations simultaneously.
But hey, who needs calculations when we have "Height-o-Matic!" Well, in this case, let's do some of that math. By solving these equations, you'll find that the height of the building is about 17.32 meters.
So, it seems our building is quite the upward performer, reaching a staggering height of 17.32 meters! Bravo, Mr. Building! Bravo!
To find the height of the building, we can use the concept of similar triangles. Let's denote the height of the building as "h" and the initial length of the shadow as "x".
We know that as the angle of elevation of the sun rays decreases from 70 degrees to 60 degrees, the shadow increases by 10 meters. This means that the ratio of the height of the building to the length of the shadow remains constant.
Using the concept of similar triangles, we have:
tan(70°) = h / x (Equation 1)
tan(60°) = (h + 10) / x (Equation 2)
Dividing Equation 2 by Equation 1, we have:
tan(60°) / tan(70°) = (h + 10) / h
Now we can solve for h:
Using the trigonometric identities tan(60°) = √3 and tan(70°) ≈ 2.747477, we have:
√3 / 2.747477 ≈ 1.732051 / 2.747477
Simplifying, we get:
0.629 ≈ 0.63057
So, (h + 10) / h ≈ 0.63057
Cross-multiplying, we have:
0.63057h ≈ h + 10
0.63057h - h ≈ 10
0.63057h ≈ 10
Dividing both sides by 0.63057, we get:
h ≈ 10 / 0.63057
h ≈ 15.867
Therefore, the height of the building is approximately 15.867 meters.