From the top of the Metro Building, the angle of elevation of the top of the Gammapro Building is 24° and the angle of depression to the foot of the Gammapro Building is 56°. If the buildings are 45 m apart, determine the height of each building to the nearest meter.
Metro: 45tan56°
Gammapro: 45(tan56°+tan24°)
It always helps in these problems to draw a diagram. Then you can see which sides of the triangle you have, and so which trig functions to use.
Of course, it also helps to review your trig functions, and study the similar examples in your text...
56
Metro: 15.58m
Gammapro: 31.16m
To determine the height of each building, we can use the concept of trigonometry, specifically the tangent function.
Let's define the variables:
h1 = height of the Metro Building
h2 = height of the Gammapro Building
From the top of the Metro Building, we have an angle of elevation to the top of the Gammapro Building, which is 24°. This means that if we draw a right triangle from the top of the Metro Building to the top of the Gammapro Building, the angle 24° will be opposite the side h2 and adjacent to the side 45m (the horizontal distance between the buildings).
Using the tangent function, we have the equation:
tan(24°) = h2/45
Solving for h2:
h2 = 45 * tan(24°)
Now, from the top of the Metro Building, we also have an angle of depression to the foot of the Gammapro Building, which is 56°. This means that if we draw a right triangle from the top of the Metro Building to the foot of the Gammapro Building, the angle 56° will be opposite the side h1 (the height of the Metro Building) and adjacent to the side 45m.
Using the tangent function again, we have the equation:
tan(56°) = h1/45
Solving for h1:
h1 = 45 * tan(56°)
Now we can substitute the values of h1 and h2 into the above equations to calculate the heights.
Finally, we round the answers to the nearest meter to get the height of each building.