A six-foot-tall person walks from the base of a broadcasting tower directly toward the tip of the shadow cast by the tower. When
the person is 132 feet from the tower and 3 feet from the tip of the shadow, the person’s shadow starts to appear beyond the tower’s shadow. What is the height of the tower?
1 answer:
Answer:
270 feet
Step-by-step explanation:
For clarity, the image below represents the problem. Let's call h the height of the tower. Notice that it forms 2 triangles that are similar to side-angle-side. So, we can calculate the higher of the tower by similar triangles:
higher1/base1 = higher2/base2
h/135 = 6/3
h/135 = 2
h = 270 ft
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Answer:
745.44 square mm
Step-by-step explanation:
The figure can be decomposed into ...
- a semicircle of radius 12.5 mm
- a rectangle 12.5 mm by 25 mm
- a triangle 12.5 mm by 30 mm
The relevant area formulas are ...
Semicircle: A = 1/2πr² = 1/2π(12.5 mm)² ≈ 245.437 mm²
Rectangle: A = LW = (12.5 mm)(25 mm) = 312.500 mm²
Triangle: A = 1/2bh = 1/2(12.5 mm)(30 mm) = 187.500 mm²
Total area of the figure is ...
245.437 +312.500 +187.500 = 745.437 . . . mm²
The area of the figure is about 745.44 square mm.
