The hurdle and runner form a right triangle (see attached picture) such that
sin(30°) = <em>h</em> / (5 ft)
and
cos(30°) = <em>x</em> / (5 ft)
where <em>h</em> is the height of the hurdle and <em>x</em> is the horizontal distance from where the runner jumps to the hurdle. So
<em>h</em> = (5 ft) sin(30°) = 5/2 ft = 2.5 ft
<em>x</em> = (5 ft) cos(30°) = (5√3)/2 ft ≈ 4.33 ft
Answer:
The answer is below
Step-by-step explanation:
a) Triangle A is attached in the image below.
The base of triangle A is 3 units and its height is 3 units. The area of a triangle is given as:
Area = (1/2) × base × height
Area of triangle A = (1/2) × base × height = (1/2) × 3 × 3 = 4.5 unit²
Area of the scaled copy = 72 unit²
Ratio of area = Area of the scaled copy / Area of triangle A = 72 unit² / 4.5 unit² = 16
Hence the scaled copy area is 16 times larger than that of triangle A.
b) For the scaled copy:
Area of the scaled copy = (1/2) × base × height = 72 unit²
base × height = 144
Since the base and height are equal
base² = 144
base = 12, also height = 12
Base of scaled copy = 12 = 4 × base of triangle A
Therefore the scale factor used is 4
