This question is incomplete, the complete question;
At 11:30 a.m. the angle of elevation of the sun for one city is 55.7°. If the height of a monument is approximately 555 ft, what is the length of the shadow it will cast at that time? Round to the nearest foot.
Answer:
the length of the shadow will be 379 ft
Explanation:
Given the data in the question and as represented in the diagram below;
height of monument = 555 ft
angle of elevation = 55.7°
From the image below, this makes a right angled triangle
we know that the some of the interior angles of a triangle is 180
so
∠ABC + ∠BCA + ∠CAB = 180°
90° + 55.7° + ∠CAB = 180°
∠CAB = 180° - 145.7°
∠CAB = 34.3°
Now, using sine rule;
BC / sinA = AB / sinC
so we substitute
BC / sin( 34.3°) = 555 / sin( 55.7° )
BC / 0.563526 = 555 / 0.826098
we cross multiply
BC × 0.826098 = 0.563526 × 555
BC × 0.826098 = 312.75693
BC = 312.75693 / 0.826098
BC = 378.595 ≈ 379 ft
Therefore, the length of the shadow will be 379 ft