from a window 25m above a street, the angle of elevation of the top of a wall on the opposite side is15°.If the angle of depression of the base of the wall from the window is 35° the width of the street? (b). the length in the opposite side?
from a window of building 4.25m above the ground, the angle of elevation of the top of a nearby building is 36.6 degrees and the angle of depression of its base is 26.2 degrees. What is the height of the nearby building?
Can someone explain how they got that answer.
yahuuuu
How to calculate the sum
To solve this problem, we will use trigonometric ratios. Let's label the given information in the problem:
- The height of the window above the street is 25m.
- The angle of elevation from the window to the top of the wall is 15 degrees.
- The angle of depression from the window to the base of the wall is 35 degrees.
Now, let's find the width of the street (b):
To determine the width of the street, imagine a right-angled triangle formed by the window, the top of the wall, and the base of the wall.
Step 1: Find the height of the wall (h):
We can use the tangent function since we have the angle of elevation. Tangent(theta) = opposite side (h) / adjacent side (25m).
tan(15°) = h / 25m
h = 25m * tan(15°)
h ≈ 6.47m (rounded to two decimal places)
Step 2: Find the length of the opposite side (a):
Since we have the angle of depression, we can use the tangent function again. Tangent(theta) = opposite side (a) / adjacent side (25m).
tan(35°) = a / 25m
a = 25m * tan(35°)
a ≈ 17.69m (rounded to two decimal places)
Step 3: Calculate the width of the street (b):
The width of the street is the difference between the lengths of the opposite side (a) and the height of the wall (h).
b = a - h
b ≈ 17.69m - 6.47m
b ≈ 11.22m (rounded to two decimal places)
Therefore, the width of the street is approximately 11.22 meters.
Now, let's find the length on the opposite side (c):
Using the Pythagorean theorem: c^2 = a^2 + h^2
c^2 = (17.69m)^2 + (6.47m)^2
c^2 ≈ 311.96m^2 + 41.89m^2
c^2 ≈ 353.85m^2
c ≈ √(353.85m^2)
c ≈ 18.8m (rounded to two decimal places)
Therefore, the length on the opposite side is approximately 18.8 meters.
here
x≈37.32∘