Round 10,387 to the nearest thousand.

But what we are given are distances between three points, A to B, B to C and A to C. When put together these make three sides (or SSS). To solve this triangle we need to use the Law of Cosines to find one angle then either the Law of Cosines or the Law of sines for as second angle. The third angle comes from subtracting the sum of the two from 180.

Let's try to find the angle between AB and BC - or angle B.

By the Law of Cosines,

cos B = AB² + BC² - AC² / 2(AB)(BC)

= 36.318² + 37.674² - 11.164² / 2(36.318)(37.674)

= 1318.997 + 1419.330 - 124.634 / 2736.489

= 2613.693 / 2736.489

= 0.95512

Through a calculator's inverse cosine (cos⁻¹) key, we have the angle as 17.229 degrees. Thus, angle B is 17.229 degrees.

To find another of the angles, we can use the Law of Sines or the Law of Cosines. The choice is yours, but let's use Law of Cosines a second time. We will use it to find angle A.

cos A = BA² + AC² - BC² / 2(BA)(AC) Notice by writing AB as BA, it tells us to make BA and AC the sides including angle A.

cos A = 36.318² + 11.164² - 37.674² / 2(36.318)(11.164)

cos A = 1318.997 + 124.634 - 1419.330 / 810.908

cos A = 24.301 / 810.908

cos A = 0.029968

Again, by a calculator's inverse cosine key, the measure of angle A is 88.28267 degrees.

Since the sum of the angles of any triangle is 180 degrees, we can find angle C by subtracting our two found angles from it.

angle A + angle B + angle C = 180

angle C = 180 - angle A - angle B by subtracting Angles A and B on both sides

angle C = 180 - 88.28267 - 17.229

angle C = 74.48833

We put these angles together - A being 88, B being 17, C being 74, and select choice A to solve the triangle.

6 0

4 years ago

1) Write an expression to represent the pattern. 19, 27, 35, 43...

garri49 [273]

Answer:

1) The expression to represent the pattern is 11 + 8n

2) The expression to represent the pattern is 80 - 9n

Step-by-step explanation:

1) * Lets study the pattern;

- 19 , 27 , 35 , 43 , ..................

∵ 27 - 19 = 8

∵ 35 - 27 = 8

∵ 43 - 35 = 8

∴ The difference is constant between each two consecutive terms

∴ It is an arithmetic sequence

* Lets take about the arithmetic sequence

- If the first term is a and the constant difference is d

∴ a1 = a , a2 = a + d , a3 = a + 2d , a4 = a+ 3d , ........

∴ an = a + (n - 1)d, where n the position of the term in the sequence

* Now we will use this rule to find the expression of our pattern

∵ a = 19 , d = 8

∴ an = 19 + (n - 1)(8) ⇒ an = 19 + 8n - 8 ⇒ an = 11 + 8n

* Lets check it;

∵ a3 = 11 + 8(3) = 11 + 24 = 35 ⇒ true

∴ The expression to represent the pattern is 11 + 8n

2) * Lets study the pattern;

- 71 , 62 , 53 , 44 , ..................

∵ 62 - 71 = -9

∵ 53 - 62 = -9

∵ 44 - 53 = -9

∴ The difference is constant between each two consecutive terms

∴ It is an arithmetic sequence

* We will use the same rule above to find the expression of the pattern

∵ a = 71 , d = -9

∴ an = 71 + (n - 1)(-9) ⇒ an = 71 + -9n + 9 ⇒ an = 80 - 9n

* Lets check it;

∵ a4 = 80 - 9(4) = 80 - 36 = 44 ⇒ true

∴ The expression to represent the pattern is 80 - 9n

8 0

4 years ago

Find the area of a square with a side of length 2 Square root of 3+6 square root of 7 inches

kodGreya [7K]

Answer:

Step-by-step explanation:

Area of a square = Length * Length

A = L²

Given the length of a square as $2\sqrt{3}+6\sqrt{7}$ inches' The area of the square will be calculated as shown;

$A = (2\sqrt{3}+6\sqrt{7})^2\\\\A = (2\sqrt{3}+6\sqrt{7})(2\sqrt{3}+6\sqrt{7})\\\\A =(2\sqrt{3})(2\sqrt{3})+(2\sqrt{3})(6\sqrt{7})+(6\sqrt{7})(2\sqrt{3})+(6\sqrt{7})(6\sqrt{7})\\\\A = 4\sqrt{9}+12\sqrt{21}+12\sqrt{21}+36\sqrt{49}\\\\A = 4(3)+24\sqrt{21}+36(7)\\ \\A = 12+24\sqrt{21}+252\\\\A = 264+24\sqrt{21}$

<em>Hence the area of the square is (264+24√21) in²</em>

8 0

3 years ago