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3 years ago

Find the length of the bold arc. Round to the nearest tenth and use 3.14 or the pi button on your calculator for pi.

Mathematics

1 answer:

Elanso [62]3 years ago

4 0

Answer:

8π yards

Step-by-step explanation:

A circle subtends a total angle of 360 ° from its center.The length of an arc is directly proportional to the angle it subtends from the circle's center. The arc's length can therefore be calculated as:

C=πd=2πr

Where C is circumference, d is diameter and r is radius. Given r as 16 yards then the arc length which is equivalent to circumference is given as

$C=\frac {90}{360}*2*\pi*16=8\pi$

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Solve for x. Enter your answer as a whole number or reduced fraction.<br><br><br><br> x = ___ a0

miv72 [106K]

Answer:

$x = \frac{1}{2}$

Step-by-step explanation:

$x = log_{e}\sqrt{e} \\ x = log_{e}e^{ \frac{1}{2} } \\ x = \frac{1}{2} log_{e}e \\ x = \frac{1}{2} \times 1 \\ x = \frac{1}{2}$

5 0

3 years ago

1. To the nearest degree, find the measure of angle A.

Assoli18 [71]

Answer:

(1) Option A is correct , The measure of angle A = 26°

(2) Option D is correct, The measure of angle B =70°

Step-by-step explanation:

(1)

In a right angle triangle figure-1 ,

* Hypotenuse(H) is always opposite the right angle and it is always the longest side of the triangle.

* Adjacent side (B) is the non-hypotenuse side that is next to a given angle A.

* Opposite side(P) is across from a given angle A.

To find the Angle A we use the Cosine ratio:

Cosine ratio states that the ratio of the adjacent side of a right triangle to the hypotenuse.

By definition of cosine ratio we have;

$\cos A = \frac{B}{H}$ ....[1]

In the figure - 1 we have B = 18 in and H = 20 in

substitute these in [1] to find angle A

$\cos A =\frac{18}{20} =\frac{9}{10} = 0.9$

$A = cos^{-1} (0.9)$

⇒ $A \approx 26^{\circ}$

therefore, the measure of angle A is, $26^{\circ}$

(2)P

In figure -2

Find the measure of angle B.

First find the side BC, using Pythagoras theorem;

Pythagoras theorem states that in the right angle triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Apply Pythagoras theorem in rt. angle ABC;

$AB^2 = AC^2+BC^2$