Mathematics, 21.11.2020 18:20 vanessasantos2004vs

3. Priya says, "I know everything about a right triangle with a 30 degree angle and a hypotenuse with length 1 cm. Here look." The other angle is 60 degrees. The leg adjacent to the 30 degree angle 0.866 cm long. The side opposite the 30 degree angle is 0.5 cm long. Han asks, "What would happen if a right triangle with a 30 degree angle has a hypotenuse that is 2 cm instead?" Help them find the missing angles and side lengths in the new triangle. Explain or show your reasoning.

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Answer from: scottmichetti

1) The measure of the third angle is 60°

2) The length of the opposite side to the angle 30° is 1 cm

3) The length of the opposite side to the third angle 60° is approximately 1.732 cm

Step-by-step explanation:

1) The given parameters are;

The known angle of a right triangle = 30°

The length of the hypotenuse = 2 cm

Given that the triangle = A right triangle, with one of the interior angles = 90°, we have;

The measure of the third angle = 180° - 90° - 30° = 60°

The measure of the third angle = 60°

2) We have that sin(30°) = 0.5 = (The length of the opposite side to the angle 30°)/(The length of the hypotenuse side)

0.5 = (The length of the opposite side to the angle 30°)/(2 cm)

∴ The length of the opposite side to the angle 30° = 2 cm × 0.5 = 1 cm

The length of the opposite side to the angle 30° = 1 cm

3) Similarly, the length of the opposite side to the third angle 60° = sin(60°) × (The length of the hypotenuse side)

∴ The length of the opposite side to the third angle 60° = (√3)/2 × 2 cm = √3 cm

The length of the opposite side to the third angle 60° = √3 cm ≈ 1.732 cm

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

Omg that is a big question and weird words and i’m only 5

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