All categories

2 years ago

A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm.

Mathematics

2 answers:

hammer [34]2 years ago

5 0

I dont think this may be right but i think it is 401

Lyrx [107]2 years ago

5 0

Answer:

Area of the triangle will be 161.70 cm²

Step-by-step explanation:

In the figure attached, in ΔABC

m∠ABC = 23°

Adjacent side BC = 27.6 cm

and hypotenuse AC = 30 cm

Area of the triangle ABC = $\frac{1}{2}\times (\text{Height})\times (\text{Base})$

= $\frac{1}{2}(AB)(BC)$

By the sine rule,

sin23° = $\frac{AB}{AC}$

AB = AC(sin23°)

= 30sin23°

= 30×(0.3907)

= 11.72 cm

Area of the triangle ABC = $\frac{1}{2}\times 11.72\times 27.6$

= 11.72×13.8

= 161.736 cm²

≈ 161.7 cm²

Therefore, area of the triangle will be 161.70 cm².

You might be interested in

Use the factor theorem to determine whether or not the first polynomial is a factor of the second

krok68 [10]

Answer/Step-by-step explanation:

Based on the factor theorem, a polynomial, x - a, is said to be a factor of another polynomial, f(x), if an only if f(a) = 0.

Using this theorem, let's determine whether each of the given first polynomial, is a factor of the second polynomial.

1. x - 1; x² + 2x + 5

By the factor theorem, x - 1 will be a factor of f(x) = x² + 2x + 5, if and only if f(1) = 0.

f(1) = 1² + 2(1) + 5

= 1 + 2 + 5

= 8

Since f(1) ≠ 0, therefore the first polynomial, x - 1, is NOT a factor of the second polynomial, x² + 2x + 5.

2. x + 1; x³ - x - 2

By the factor theorem, x + 1 will be a factor of f(x) = x³ - x - 2, if and only if f(-1) = 0.

f(1) = -1³ - (-1) - 2

= -1 + 1 - 2

= -2

Since f(-1) ≠ 0, therefore the first polynomial, x + 1, is NOT a factor of the second polynomial, x³ - x - 2.

3. x - 4; 2x³ - 9x² + 9x - 20

By the factor theorem, x - 4 will be a factor of f(x) = 2x³ - 9x² + 9x - 20, if and only if f(4) = 0.

f(4) = 2(4)³ - 9(4)² + 9(4) - 20

= 128 - 144 + 36 - 20

= 0

Since f(4) = 0, therefore the first polynomial, x + 4, is a factor of the second polynomial, 2x³ - 9x² + 9x - 20.

4. a - 1; a³ - 2a² + a - 2

By the factor theorem, a - 1 will be a factor of f(a) = a³ - 2a² + a - 2, if and only if f(1) = 0.

f(1) = 1³ - 2(1)² + 1 - 2

= 1 - 2 + 1 - 2

= -2

Since f(1) ≠ 0, therefore the first polynomial, a - 1, is NOT a factor of the second polynomial, a³ - 2a² + a - 2.

5. y + 3; 2y³ + y² - 13y + 6

By the factor theorem, y + 3 will be a factor of f(y) = 2y³ + y² - 13y + 6, if and only if f(-3) = 0.

f(-3) = 2(-3)³ + (-3)² - 13(-3) + 6

= -54 + 9 + 39 + 6

= 0

Since f(-3) = 0, therefore the first polynomial, y + 3, is a factor of the second polynomial, 2y³ + y² - 13y + 6.

7 0

2 years ago

Which values of x and y would make the following expression represent a real number? (4+5i)(x+yi)

algol [13]

Answer:

So x=4 and y=-5 would work.

Step-by-step explanation:

When you multiply complex conjugates, you get a real result.

Example:

$(a+bi)(a-bi)=a^2-b^2i^2=a^2+b^2$

I replace $i^2$ with -1 since $i^2=-1$ .

$a^2+b^2$ is a real number (there is no imaginary part, no i).

So what is the conjugate of 4+5i?

4-5i

So x=4 and y=-5 would work.

A multiple of the complex conjugate would work as well.

$(a+bi)(ca-cbi)$

$c(a+bi)(a-bi)$

$c(a^2-b^2i^2)$

$c(a^2+b^2)$

This is still a real number; there is no imaginary part,no i.

5 0

2 years ago

I dont know how to do this... Please answer and explain how. Thanks!

kozerog [31]

Answer:

1620.2

Step-by-step explanation:

V=3/4(pi)r^3

V=3/4(3.14)(512)

3 0

2 years ago

According to the Rational Roots Theorem, which statement about f(x) = 25x7 – x6 – 5x4 + x – 49 is true? Any rational root of f(x

Darya [45]

Answer:

Any rational root of f(x) is a factor of -49 divided by a factor of 25

Step-by-step explanation:

The Rational Roots Theorem states that, given a polynomial

$p(x) = a_nx^n+a_{n-1}x^{n-1}+\ldots+a_2x^2+a_1x+a_0$

the possible rational roots are in the form

$x=\dfrac{p}{q},\quad p\text{ divides } a_0,\quad q\text{ divides } a_n$

5 0

2 years ago

Read 2 more answers

In a certain recipe that produces enough for 8 servings, 1/2 cup of sugar is required. If you were asked to expand this recipe s

Furkat [3]

We have to apply the rule of three

8 servings--------------------1/2 cup of sugar
26 servings--------------------- x

x=(26 servings*(1/2) cup of sugar) / 26 servings=1.625 cup of sugar.

7 0

2 years ago

Read 2 more answers