Step-by-step explanation:
there is a right-angled triangle "hovering" 1.74 m above the ground.
its Hypotenuse (the side opposite of the 90 degree angle) is the line of sight from the eye to the top of the skyscraper.
the legs are the ground distance (369 m) of Sophia from the skyscraper and the height of the skyscraper.
besides the one side length we know 2 angles : the 90° angle between the ground distance and the height, and the 44° between the ground distance and the line of sight.
as the sum of all angles in a triangle is always 180°, we also know the third angle between the line of sight and the height : 180 - 90 - 44 = 46°
now we can use the law of sines to get the missing side lengths :
a/sin(A) = b/sin(B) = c/sin(C)
where the angles are always opposite of the sides.
the 44° angle is opposite of the height.
the 46° angle is opposite of the ground distance.
so,
height/sin(44) = 369/sin(46)
height = 369 × sin(44)/sin(46) = 356.3391579... m
the get the full height of the skyscraper we need to add to 1.74 m our triangle was hovering above ground.
therefore, the height of the skyscraper is
356.3391579... + 1.74 = 358.0791579... m ≈ 358.1 m
The height of the skyscraper for the considered case is evaluated being of 358 meters approx.
You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.
Remember that we assume that building is vertical to the ground. This means, there is 90° formation.
For this case, referring to the figure attached below, we get:
The height of the skyscraper = h = length of ED (which is h - 1.74 meters) + 1.74 meters
Using the tangent ratio for triangle CDE, from the perspective of angle of elevation, we get:
[tex]\tan(44^\circ) = \dfrac{|ED|}{|CD|} = \dfrac{h-1.74}{|AB|} \\0.9656 \approx \dfrac{h-1.74}{369}\\\\h \approx 0.9656 \times 369 + 1.74 \approx 358 \: \rm m[/tex]
(from calculator, we obtained [tex]tan(44^\circ) \approx 0.9656[/tex] )
Thus, the height of the skyscraper for the considered case is evaluated being of 358 meters approx.
Learn more about tangent ratio here:
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