Select the best answer for the question

If t = 18 and r = 12, find S. Round to the nearest tenth.

choli [55]

Answer: S ≈ 48.2°

Step-by-step explanation:

We can use trigonometry functions to solve.

Looking at angle S, t = 18 is the hypotenuse and r = 12 is the adjacent side. This means we can use the cosine function.

$\displaystyle cos(S) = \frac{\text{adjacent side}}{\text{hypotenuse }}=\frac{12}{18}$

$\displaystyle cos^{-1} (cos(S)) = (\frac{\text{adjacent side}}{\text{hypotenuse }}=\frac{12}{18})cos^{-1}$

$S = 48.189685...\\S \;$\approx$\; 48.2^{\circ}$

3 0

1 year ago

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Find the lateral area of the come in terms of pi.

Norma-Jean [14]

The answer should be 12x cm power of 2

4 0

3 years ago

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A certain positive number is multiplied by 4, and then the result is subtracted from the original number. The result is 21 less

stira [4]

Answer:

The number is 7

Step-by-step explanation:

certain positive number: x

x is multipled by 4:

4x

result of this is subtracted from the original number:

so original number minus 4x,

x - 4x

the result is 21 less than 0, this means negative 21

x - 4x = 0 - 21 = -21

do algebra:

-3x = -21

multiply both sides by -1

3x = 21

divide both sides by 3

x=7

(certain positive number: x) is equal to 7

4 0

3 years ago

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What is the translation from quadrilateral IJK to quadrilateral I'J’K’

liberstina [14]

Answer:

The translation from triangle IJK to triangle I'J'K' is $T_{(2, 6)}$ which is 2 units to the right and 6 units up

Step-by-step explanation:

The coordinates of triangle JKI are;

J has coordinates (1, - 1)

K has coordinates (1, - 4)

I has coordinates (-3, - 2)

While, the coordinates of translation triangle J'K'I' are;

J' has coordinates (3, 5)

K' has coordinates (3, 2)

I' has coordinates (-1, 4)

Which give the translation as follows

Translation in the y-coordinate (y values);

For J = 5 - (-1) = 6

For K = 2 - (-4) = 6

For I = 4 - (-2) = 6

Translation in the x-coordinate (x values);

For J = 3 - 1 = 2

Therefore, the translation from triangle IJK to triangle I'J'K' is T(2, 6) which is 2 units to the right and 6 units up

6 0

3 years ago

Given the line a and b are parallel angles 1 and5 are congruent because they are

kakasveta [241]

Answer:

Step-by-step explanation:

When two lines intersect they form two pairs of opposite angles, A + C and B + D. Another word for opposite angles are vertical angles.

figure51

Vertical angles are always congruent, which means that they are equal.

Adjacent angles are angles that come out of the same vertex. Adjacent angles share a common ray and do not overlap.

figure52

The size of the angle xzy in the picture above is the sum of the angles A and B.

Two angles are said to be complementary when the sum of the two angles is 90°.

figure53

Two angles are said to be supplementary when the sum of the two angles is 180°.

figure54

If we have two parallel lines and have a third line that crosses them as in the ficture below - the crossing line is called a transversal

When a transversal intersects with two parallel lines eight angles are produced.

figure55

The eight angles will together form four pairs of corresponding angles. Angles 1 and 5 constitutes one of the pairs. Corresponding angles are congruent. All angles that have the same position with regards to the parallel lines and the transversal are corresponding pairs e.g. 3 + 7, 4 + 8 and 2 + 6.

Angles that are in the area between the parallel lines like angle 2 and 8 above are called interior angles whereas the angles that are on the outside of the two parallel lines like 1 and 6 are called exterior angles.

Angles that are on the opposite sides of the transversal are called alternate angles e.g. 1 + 8.

All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent.

Example

figure56

The picture above shows two parallel lines with a transversal. The angle 6 is 65°. Is there any other angle that also measures 65°?

6 and 8 are vertical angles and are thus congruent which means angle 8 is also 65°.

6 and 2 are corresponding angles and are thus congruent which means angle 2 is 65°.

6 and 4 are alternate exterior angles and thus congruent which means angle 4 is 65°.

4 0

3 years ago