Mathematics, 12.03.2020 23:56 lisa5250

40 Points ♥ Trigonometry

The area of an isosceles triangle is 100cm².
Calculate the perimeter of the triangle given that one of the angles is π/6 rad.

Answers: 3

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Answer from: gporter9200

Case 1: 50.35 cm

Case 2: 56.715 cm

Step-by-step explanation:

AB = AC;

½ X AH x BC = 100 cm2

=> AH x BH = 100 cm2

=> AH = 100/BH

Case 1: (BAC)= $\pi$ /6

S = ½ x AB x AC x sin (BAC) = 100 cm2

AB^2 x sin $\pi$ /6 = 200

=> AB^2 x ½ = 200

=> AB = 20 cm = AC

BC^2 = AB^2 + AC^2 – 2 x AB x AC x cos (BAC) = 202 + 202 – 2 x 20 x 20 x $\sqrt{3}$ /2 = (800 - 400 $\sqrt{3}$ ) cm

=> BC = 10.35 cm

Perimeter: AB + AC + BC = 20 + 20 + 10.35 = 50.35 cm

Case 2: (ABC) = $\pi$ /6 => (BAC) = 2 $\pi$ /3

S = ½ x AB x AC x sin (BAC) = 100 cm2

AB^2 x sin 2 $\pi$ /3 = 200

=> AB^2 x $\sqrt{3}$ /2 = 200

=> AB^2 = 400/ $\sqrt{3}$

=> AB = AC = 15.197 cm

BC^2 = AB^2 + AC^2 – 2 x AB x AC x cos (BAC) = 400/ $\sqrt{3}$ + 400/ $\sqrt{3}$ – 2 x 400/ $\sqrt{3}$ x (-1/2) = 692.82 cm

=> BC = 26.321

Perimeter: AB + AC + BC = 15.197 + 15.197 + 26.321 = 56.715 cm

40 Points ♥ Trigonometry The area of an isosceles triangle is 100cm². Calculate the perimeter of the

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

Answer from: Quest

step-by-step explanation: the answer is 27. first multiply .32 by 25 which equals 8. then add 8 to 25 which gives you 33. then you subtract that from 6 since she gave 6 to her brother.

,, add !

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40 Points ♥ Trigonometry

The area of an isosceles triangle is 100cm².
Calculate th...