Answer:
∠A ≈ 66°
∠B ≈ 24°
AC ≈ 1.2
Step-by-step explanation:
SOH CAH TOA and the Pythagorean theorem are useful tools for solving right triangles. The first tells you ...
Sin = Opposite/Hypotenuse
For ∠A, that means ...
sin(A) = BC/AB = 2.7/2.95
The inverse sine function (sin⁻¹ or arcsin) is used to find the angle from its sine value, so ...
A = arcsin(2.7/2.95) ≈ 66°
Likewise, the ratio for angle B involves the adjacent side:
Cos = Adjacent/Hypotenuse
cos(B) = BC/AB = 2.7/2.95
B = arccos(2.7/2.95) ≈ 24°
Of course, angles A and B are complementary, so once you know angle A, you know that angle B is ...
∠B = 90° -∠A = 90° -66° = 24°
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The Pythagorean theorem can be used to find the unknown side. It tells you ...
AB² = AC² + BC²
2.95² = AC² + 2.7²
AC = √(2.95² -2.7²) ≈ 1.2
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These calculations are shown in the attachment using a TI-84 graphing calculator set to degrees mode. Any scientific or graphing calculator will do.
Answer:
x = 83 degrees
Step-by-step explanation:
35 + 28 = 63
63 + 34 = 97
180 - 97 = 83
Answer:
Angle KMP is congruent to angle LNP because they are alternate interior angles.
Step-by-step explanation:
Alternate interior angles are angles inside the parallel lines and on opposite sides of the transversal.
KM and NL are parallel to one another. KMP and LNP both fall between the parallel lines; this makes them interior.
KL is a transversal for the two parallel lines. KMP and LNP are on opposite sides of the transversal; this makes them alternate.
Therefore they are alternate interior angles.
Answer:
<u>-53</u>, f(n) = -6(n-1) + 13
Step-by-step explanation:
given the equation to this linear/arithmetic sequence for the nth term: f(n) = -6(n-1) + 13
f(12) = -6(12-1) + 13
f(12) = -6(11) + 13
f(12) = -66 + 13
f(12) = -53
*substitute and simplify*
______________
f(n) = f(1) + d(n-1)
given f(1) = 13, f(2) = 7, and f(3) = 1
7-13 = 1-7 = <u>-6</u> = d
= f(1) + d(n-1)
f(1) = <u>13</u> so
the equation must be f(n) = <u>13</u> <u>-</u><u> </u><u>6</u>(n-1) or -6(n-1) + 13
<span>Simplifying
2x + 5 + 6x + -1 = 120
Reorder the terms:
5 + -1 + 2x + 6x = 120
Combine like terms: 5 + -1 = 4
4 + 2x + 6x = 120
Combine like terms: 2x + 6x = 8x
4 + 8x = 120
Solving
4 + 8x = 120
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + 8x = 120 + -4
Combine like terms: 4 + -4 = 0
0 + 8x = 120 + -4
8x = 120 + -4
Combine like terms: 120 + -4 = 116
8x = 116
Divide each side by '8'.
x = 14.5
Simplifying
x = 14.5</span>
