Can anyone please please help me with this,this is a quiz

In the 30-60-90 triangle below, side s has a length of ___ and side q has a length of ___.

larisa [96]

Answer:

The answer is D.

Step-by-step explanation:

The side lengths for this special triangle is represented with x, x $\sqrt{3}$ , and 2x

if the side length that sees 90 degrees is 10 (2x and x = 5 in this case)

so s (the side length that sees 30 degrees) is = 5

and q (the side length that sees 60 degrees) = 5 $\sqrt{3}$

6 0

3 years ago

The diagram shows how cos θ, sin θ, and tan θ relate to the unit circle. Copy the diagram and show how sec θ, csc θ, and cot θ r

DIA [1.3K]

Copy the diagram and show how sec θ, csc θ, and cot θ relate to the unit circle.

The representation of the diagram is shown if Figure 1. There's a relationship between sec θ, csc θ, and cot θ related the unit circle. Lines green, blue and pink show the relationship.

a.1 First, find in the diagram a segment whose length is sec θ.

The segment whose length is sec θ is shown in Figure 2, this length is the segment $\overline{OF}$ , that is, the line in green.

a.2 Explain why its length is sec θ.

We know these relationships:

(1) $sin \theta=\frac{\overline{BD}}{\overline{OB}}=\frac{\overline{BD}}{r}=\frac{\overline{BD}}{1}=\overline{BD}$

(2) $cos \theta=\frac{\overline{OD}}{\overline{OB}}=\frac{\overline{OD}}{r}=\frac{\overline{OD}}{1}=\overline{OD}$

(3) $tan \theta=\frac{\overline{FD}}{\overline{OC}}=\frac{\overline{FC}}{r}=\frac{\overline{FC}}{1}=\overline{FC}$

Triangles ΔOFC and ΔOBD are similar, so it is true that:

$\frac{\overline{FC}}{\overline{OF}}= \frac{\overline{BD}}{\overline{OB}}$ 

∴ $\overline{OF}= \frac{\overline{FC}}{\overline{BD}}= \frac{tan \theta}{sin \theta}= \frac{1}{cos \theta} \rightarrow \boxed{sec \theta= \frac{1}{cos \theta}}$ 

b.1 Next, find cot θ

The segment whose length is cot θ is shown in Figure 3, this length is the segment $\overline{AR}$ , that is, the line in pink.

b.2 Use the representation of tangent as a clue for what to show for cotangent.

It's true that:

$\frac{\overline{OS}}{\overline{OC}}= \frac{\overline{SR}}{\overline{FC}}$

But:

$\overline{SR}=\overline{OA}$
$\overline{OS}=\overline{AR}$

Then:

$\overline{AR}= \frac{1}{\overline{FC}}= \frac{1}{tan\theta} \rightarrow \boxed{cot \theta= \frac{1}{tan \theta}}$

b.3 Justify your claim for cot θ.

As shown in Figure 3, θ is an internal angle and ∠A = 90°, therefore ΔOAR is a right angle, so it is true that:

$cot \theta= \frac{\overline{AR}}{\overline{OA}}=\frac{\overline{AR}}{r}=\frac{\overline{AR}}{1} \rightarrow \boxed{cot \theta=\overline{AR}}$

c. find csc θ in your diagram.

The segment whose length is csc θ is shown in Figure 4, this length is the segment $\overline{OR}$ , that is, the line in green.

3 0

4 years ago

Abdullah is kicking a soccer ball into the air. The path of the soccer ball can be modeled by a quadratic equation where the poi

kirill [66]

9514 1404 393

Answer:

A. 0 = −(x−6)^2+12

Step-by-step explanation:

The vertex form of a quadratic equation is ...

y = a(x -h)² +k . . . . . . for vertex (h, k) and scale factor 'a'

When the given vertex (h, k) = (6, 12) is used, we find the form of the equation to be ...

y = a(x -6)² +12

The ball will be on the ground when y = 0. Here, the vertical scale factor 'a' is -1, so the equation representing the ball being on the ground is ...

0 = -(x -6)² +12 . . . . . . matches choice A

5 0

3 years ago

Why wealthy colonists used the Africans as workers? help asp

Vlad1618 [11]

Answer:

they provided cheap labour

Step-by-step explanation:

this is because Africans were sold as slaves to the rich colonialists.

4 0

3 years ago

6% of what number is 270? 4,500 450 45 4.5

Gnoma [55]

So to solve this problem, we can either do guess and check, or solve an equation.

Let's do the equation, since it will work for all problems, even when you're not given a list of possible answers.

So, to begin, let's define our unknown.

We can represent the number as "n"

So, 6 percent of "n" is equal to 270

To find a "percent" of a number, you need to multiply the number by the percentage.

So, 6 percent as a decimal is .06

This is because a percent is a fraction divided by 100 (6/100)

$.6\times n=270\\\n=270\div.6\\n= 4500$

The number is 4,500

7 0

3 years ago