the hypotenuse of a 30-60-90 triangle is 10. Find the perimeter.?

Answer 1

let

a = Opposite side

b = adjacent side

10 = hypotenuse

sin30 = degrees

cos30 = degrees

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Solving for the opposite side

sinθ = a/10

sin30 = a / 10

10sin30 = 10(a/10)

10sin30 = a

10(.5) = a

5 = a

The answer is a = 5

The opposite side = 5

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Solving for the adjacent side

cosθ = b/10

cos30 = b/10

10cos30 = 10(b/10)

10cos30 = b

10(0.866025404) = b

8.660254038 = b

The answer is b = 8.66 rounded to two decimal places.

The adjacent side is 8.66

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The perimeter is

10 + 5 + 8,66 = 23.66

The perimeter is 23.66

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Answer 2

considering you're staring at particular extraordinary triangles, you may use the actuality that the 30 degree attitude is on the midsection of the hexagon. In a 30-60-ninety triangle, the facet opposite the 30 is = one million/2 the hypotenuse. The hypotenuse is 183. So, the facet opposite the 30 degree attitude is one million/2 that, or ninety one.5. Now multiply by utilising 12 to get 1098.

Answer 3

This requires basic trigonometry. The sine of an angle in a right triangle is defined to be the length of the opposite side divided by the length of the hypotenuse.

So, the side opposite the 30 deg angle divided by 10 = sin (30) = 0.5, and multiplying both sides by 10 gives opp = 5.

Similarly adj / hyp = sin (60) = 0.866, and adj = 8.66.

The perimeter is 10 + 5 + 8.66 = 23.66.

You could also solve this problem using cosines.

Answer 4

6+8+10=24

Answer 5

This is half of a 60-60-60 triangle, so short side is 5.
from Pythagoras, squares of sides in right triangle, here ratios of sides are 1 : (sq.rt.3) : 2
so sides are 5 : (5 x 1.732) : 10.
perimeter is 5 + 8.66 + 10 = 23.66

Answer 6

10+5+8.66 = 23.66, or to be precise 15+5sqrt(3)

let the side opposite the 30 angle be x, and the other one y

x/10 = sin(30) = 0.5

Therefore x = 5

By pythagoras y^2 + 5^2 = 10^2 so:

y = +sqrt(10^2-5^2) = sqrt(75) = 5sqrt(3) = 8.66025

The perimeter equals the sum of the 3 sides:

Perimeter =10+5+5sqrt(3)

Answer 7

By pythagora's theorem:
a*a + b*b=c*c (a,b,c are sides)
ht.=csin(60 deg.)
base=ccos(60 deg.)

perimeter=10+10*(3^0.5)/2 + 10*(0.5)
=10+8.66+5=23.66 units