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If a 76-foot flagpole casts a shadow 60 feet long, what is the angle of elevation of the sun? Give your answer to the nearest tenth of a degree. Ex: 34.5, 67.2. [ans] degrees



Answer :

reinhard10158

Step-by-step explanation:

this creates a right-angled triangle with the flagpole and the shadow being the 2 legs, and the distance top of flagpole to the end of the shadow is the Hypotenuse.

per Pythagoras we have then

Hypotenuse² = 76² + 60² = 5776 + 3600 = 9376

Hypotenuse = 96.8297475... ft

now, per law of sine

a/sinA = b/sinB = c/sinC

with a, b, c being the sides of the triangle, A, B, C being the corresponding opposite angles,

we have

flagpole length/sin(bottom right angle = angle of elevation) = Hypotenuse / sin(90°).

sin(90°) = 1

so,

76/sin(angle of elevation) = 96.8297475.../1

sin(angle of elevation) = 76/96.8297475... =

= 0.784882766...

angle of elevation = 51.70983681...° ≈ 51.7°

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