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1 year ago

The height h of the equilateral triangle below is given by y= 5 cot theta where theta = 30 degrees

Mathematics

1 answer:

brilliants [131]1 year ago

6 0

To solve this we can take two different approaches:

1. We can substitute theta by 30° and evaluate our expression using a calculator:
$y=5cot( \alpha )$
$y=5cot(30)$
$y=8.7$

2. We can use the unitary circle and the fact that $cot \alpha = \frac{cos( \alpha }{sin( \alpha )}$ , so we can rewrite our expression as follows:
$y=5cot( \alpha )$
$y=5 \frac{cos( \alpha )}{sin( \alpha )}$
$y= \frac{cos(30)}{sin(30)}$
From our unitary circle we can check that $cos(30)= \frac{ \sqrt{3} }{2}$ and $sin(30)= \frac{1}{2}$ .
Lets replace those values in our expression and simplify:
$y= \frac{ 5(\frac{ \sqrt{3} }{2})}{ \frac{1}{2} }$
$y=5 \sqrt{3}$
$y=8.7$

Either way we can conclude that the correct answer is: D)8.7

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Seth is using the figure shown below to prove the Pythagorean Theorem using triangle similarity: In the given triangle PQR, angl

Naily [24]

Answer:

Part A: $\triangle RPQ \sim \triangle RSP$

Part B. All angles are same, so the triangles are similar.

Part C. RP = 8

Step-by-step explanation:

We are given a right angled triangle $\triangle RPQ$ with $\angle P = 90^\circ$ .

PS is perpendicular to the hypotenuse RQ of $\triangle RPQ$ and S lies on RQ.

Part A:

To identify the pair of similar triangles.

$\triangle RPQ \sim \triangle RSP$ .

Part B:

To identify the type of similarity.

Kindly refer to the image attached in the answer area.

Let us consider the triangles $\triangle RPQ \ and\ \triangle RSP$ .

$\angle RSP =\angle RPQ =90^\circ$

Also, $\angle R$ is common to both the triangles under consideration.

Now, we can see that two angles of two triangles are equal.

So, third angle of the two triangles will also be same.

i.e. All three angles of two triangles $\triangle RPQ \ and\ \triangle RSP$ are equal to each other.

So, by A-A-A (Angle - Angle - Angle) similarity, we can say that $\triangle RPQ \sim \triangle RSP$ .

Part C:

RS = 4

RQ = 16, Find RP.

There is one property of similar triangles that:

The ratio of corresponding sides of two similar triangles is equal.

i.e.

$\dfrac{RS}{RP} = \dfrac{RP}{RQ}\\\Rightarrow RP ^2 = RS \times RQ\\\Rightarrow RP ^2 = 4 \times 16\\\Rightarrow RP ^2 = 64\\\Rightarrow \bold{RP = 8\ units}$

5 0

2 years ago

What is the smallest positive multiple of $32$?

Artemon [7]

Answer:

2 is the smallest positive multiple of $32$

explanation:

hope it helps, btw i dont have step-by-step explanation becuase i already have a answer. 

its you're choice if you're going to copy my answer. correct me if im wrong naman. 

3 0

1 year ago

Which statement about the value of x is true?

icang [17]

Answer: x > 38

In this case, x is a exterior angle of the triangle. The exterior angle of a triangle is the sum of the nonadjacent interior angles of the triangle.

Therefore:
x = 38 + 39
x = 77

77 > 38
x > 38

3 0

2 years ago

Read 2 more answers

Two horses are ready to return to their barn after a long workout session at the track. the horses are at coordinates H(1,10) an

ss7ja [257]

The given information are the coordinates of points H, Z and B. So, the first step to do is to plot these points on a Cartesian plane as shown in the attached picture. We can deduce visually that horse Z is closer to the barns than horse H. But, to further justify the answer, we have to provide the magnitude of the distance of horses H and Z to barn B. In this approach, we use the distance formula:

d = √(x₂ - x₁)² + (y₂ - y₁)²

Use the coordinates of the two points to know their linear distances. These are represented by the red and green lines for each of the horses.

Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = 19.4165

Since the scale is 1 unit = 100 meters, the actual distance between horse H and barn B is 19.416*100 = 1,941.65 meters

Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = 16.4012

Since the scale is 1 unit = 100 meters, the actual distance between horse Z and barn B is 16.4012*100 = 1,640.12 meters

Comparing the distances: 1,941.65 meters > 1,640.12 meters. Therefore, it justifies that horse Z is nearer to the barn.

4 0

1 year ago

A certain right triangle with integer side lengths has perimeter $72$. What is its area?

JulijaS [17]

Answer: 216 square units

====================================================

Explanation:

A common pythagorean triple you may be familiar with is the 3-4-5 right triangle. This has two legs of 3 and 4, and a hypotenuse of 5. The perimeter is 3+4+5 = 7+5 = 12. Note how this is a factor of 72.

If we multiply the perimeter (12) by 6, then 12*6 = 72. So we have scaled the triangle by a factor of 6. Each length is 6 times longer

the side length 3 becomes 3*6 = 18

the side length 4 becomes 4*6 = 24

the side length 5 becomes 5*6 = 30

The new perimeter is 18+24+30 = 42+30 = 72

The last step is to find the area. The two legs of this triangle are the base and height

area = 0.5*base*height

area = 0.5*18*24

area = 9*24

area = 216

-----

Or you could find the area of the 3-4-5 right triangle to get

area = 0.5*base*height = 0.5*3*4 = 6

then multiply by 36 to get 6*36 = 216. The 36 is the square of the scale factor 6 we applied above. The new lengths are 6 times longer, so the new area is 6^2 = 36 times larger.

7 0

1 year ago