What is the length of the missing leg

Mathematics

1 answer:

sp2606 [1]3 years ago

8 0

Answer:

4.33

Step-by-step explanation:

1. Pythagoras Theorem

$25 = \sqrt{3^{2}+b^{2}}$

2. Find b

$5 = 3^{2}+b^{2}$

$b^{2}$ = $5-3^{2}$ = $5-9$ = -4

but sqrt(-4) is not possible

b ≅ 4

OR (Require trig knowledge)

1. Sine Rule

$\frac{a}{sin\alpha}=\frac{b}{sin\beta}=\frac{c}{sin\pi }$

2. Plug in numbers

$\frac{5}{sin90}=\frac{b}{sin60}=\frac{3}{sin30}$

b ≅ 4.33

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Phoenix [80]

Not sure if this is how your teacher wants it, but here is how I would approach it in high school geometry:

To find the area of a rectangle, you need the base and the height.

The radius is 28 mm however the radius only covers half of one circle. Multiply 28 by 2 to get the length of one circle (56) and multiply 56 by 2 to get the length of your base of your rectangle (112).

Now to find the height: the center of the circles creates an equilateral triangle with the side length of 2r or 56 in this case. This means each angle of that triangle is 60 degrees, and when split in half, this creates two triangles both with angles of 30, 60, and 90. The altitude of this triangle is r√3 because of the “special right triangle rule” or 28√3 in this case. This comes to 48.497 mm. To find the remaining length of the height, you can use the radii of the top and bottom circle which add to 56. Add this to the previous number. So...

Height: 104.497
Base: 112

Now multiply the base times height to get:

216.497 mm.

Hope that helps!

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3 years ago

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wolverine [178]

Answer:

See steps below

Step-by-step explanation:

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