At : a. m. the angle of elevation of the sun for one city is . If the height of a monument is approximately , what is the length of the shadow it will cast at that time? Round to the nearest foot.

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.

the length of the shadow will be 379 ft

Step-by-step 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

i think it might be a but you might want a second opinion