FROM A WINDOW 9M ABOVE GROUND OF HOUSE IN A STREET ANGLES OF ELEVATION AND DEPRESSION OF TOP AND FOOT OF ANOTHER HOUSE ON OPPOSITE SIDE OF STREET ARE 30DEGREE AND 60DEGREE FIND HEIGHT OF OPPOSITE HOUSE AND WIDTH OF STREET.
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To find the height of the opposite house and the width of the street, we can use trigonometric ratios and consider the given angles of elevation and depression.
Let's denote the height of the opposite house as h and the width of the street as w.
Step 1: Determine the distance between the window and the opposite house
Since we know the height of the window above the ground is 9 meters, we can form a right-angled triangle with the distance from the window to the opposite house as the hypotenuse. Let's call this distance d.
Using the angle of depression of 60 degrees, we can write the trigonometric ratio:
tan(60) = h / d
Simplifying this equation, we get:
√3 = h / d ---(1)
Step 2: Determine the distance between the foot of the window and the opposite house
Let's call this distance x. From the given information, the angle of elevation is 30 degrees. Again, we can form a right-angled triangle with the distance x as the adjacent side and the height of the window above the ground as the opposite side.
Using the angle of elevation of 30 degrees, we can write the trigonometric ratio:
tan(30) = 9 / x
Simplifying this equation, we get:
1/√3 = 9 / x
1 = 9√3 / x
x = 9√3 ---(2)
Step 3: Find the width of the street
The width of the street (w) is simply twice the distance x, as it forms a straight line across the street.
w = 2 * x
w = 2 * 9√3
w = 18√3 ---(3)
Step 4: Substitute the value of x from equation (2) into equation (1) to find the height of the opposite house.
√3 = h / (9√3)
h = 9 ---(4)
Therefore, the height of the opposite house is 9 meters, and the width of the street is 18√3 meters.
Width = 3×1.732 m
Height = 12m
If the width of the street is w and the height of the other house is h, then if you draw a diagram, it should be clear that
9/w = tan 60°
(h-9)/w = tan 30°
Now you can easily find w, and then h.