All categories

3 years ago

Find the length of side x in simplest radical form with a rational denominator.

Mathematics

1 answer:

alekssr [168]3 years ago

4 0

Answer:

$x = \frac{2*\sqrt{3}}{3}$

Step-by-step explanation:

Reference angle = 30°

Opposite side = x

Adjacent side = 2

Apply the tan trigonometric function, thus:

$tan (30) = \frac{opp}{adj}$

$tan (30) = \frac{x}{2}$

$2 * tan (30) = x$

$2 * \frac{1}{sqrt{3}} = x$ (tan 30 = 1/√3)

$\frac{2}{sqrt{3}} = x$

Rationalize

$\frac{2* \sqrt{3}}{sqrt{3} * \sqrt{3}} = x$

$\frac{2*\sqrt{3}}{3} = x$

You might be interested in

Evaluate cos0 if sin0= sqrt(5)/3 a. 9/5 b. 2/3 c. 5/9 d. 3/2

Evgesh-ka [11]

Solution given:

$\sin( \alpha ) = \frac{\sqrt{5} }{3}$

P=√5

h=3

b= $\sqrt{3 {}^{2} - \sqrt{5} {}^{2} }$

b=2

$\cos( \alpha ) = \frac{b}{h} = \frac{2}{3}$

Note

$\alpha = 0$

b:⅔

8 0

3 years ago

You are about to attack an orc in a role playing game. You will throw two dice, one numbered 1 to 7 and the other with letters A

Nataly_w [17]

0 because h isn’t on the dice

3 0

3 years ago

What is the postulate?

ICE Princess25 [194]

Suggest or assume the existence, fact, or truth of something as a basis for reasoning, discussion, or belief.

4 0

3 years ago

Please, Help. the answer isn't 30°

vagabundo [1.1K]

The missing angle of the right triangle ABC has a measure of 30°. (Correct answer: A)

<h3>How to find a missing angle by triangle properties</h3>

Triangles are geometrical figures formed by three sides and whose sum of internal angles equals 180°. There are two kind of triangles existing in this question: (i) Right triangles, (ii) Isosceles triangles.

Right triangles are triangles which one of its angles equals 90° and isosceles triangles are triangles which two of its sides have equal measures.

According to the statement, we know that triangle BQR is an isosceles triangle, whereas triangles ABC, ANB and NBC are right triangles. Based on the figure attached below, we have the following system of linear equations based on right triangles ABC and NBC:

2 · x + 90 + θ = 180 (1)

(90 - x) + 90 + θ = 180 (2)

By equalizing (1) and (2) we solve the system for x:

2 · x = 90 - x

3 · x = 90

x = 30

And by (1) we solve the system for θ:

θ = 180 - 2 · x - 90

θ = 30

The missing angle of the right triangle ABC has a measure of 30°. (Correct answer: A) $\blacksquare$

To learn more on right triangles, we kindly invite to check this verified question: brainly.com/question/6322314

8 0

3 years ago

A fencing company charges $22 per foot to install a wood fence. How much will it cost to install a wood fence around a rectangul

borishaifa [10]

20+20+38+38=116

116×22 = 2552

It will cost $2,552 to install the wood fence.

4 0

3 years ago