Answer:
There are 157 ft. above the bottom of the gorge
Explanation:
Cliff 1 (h) = 172ft.
Cliff 2(h) = 112 ft
Height difference between the cliffs: 172ft. -112 ft. = 60 ft
Width of the gorge = 80 ft
In this problem a right triangle is formed where the hypotenuse (T) is represented by the trestle's length, the width of the gorge is one of the legs and the leg opposite the angle (Ф) is represented by the difference in height between the cliffs.
T=[tex]\sqrt{L_1^2 + L_2^2 } =\sqrt{80^2 + 60^2} =\sqrt{10,000} =100 ft[/tex]
3/4 T = 3/4(100) = 75ft.
Calculating the height of the train from the lowest cliff, we will use the proportion of the sine of the angle that forms the trestle with the horizontal.
sin(Ф)=[tex]\frac{60}{100} = \frac{x}{75}[/tex]
x=[tex]\frac{60*75}{100}=45ft[/tex]
In order to know the height from the bottom of the cliff, we must add its height to this value.
h= 45ft. + 112ft. = 157 ft.
