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1 year ago

Which statement best explains whether △ABC is similar to △DEF?

Mathematics

1 answer:

Elena L [17]1 year ago

8 0

The statement which best describes the similarity of the two triangles is; Choice D; There is not enough information to determine whether the triangles are similar.

<h3>Which statement best explains whether △ABC is similar to △DEF?</h3>

The two triangles given in the task content are expected to be assessed to determine if they are similar.

From the concept of congruence in triangles, two triangles are congruent only if all 3 angle measures in one are similar to that in the other, or if the ratio of all corresponding pairs of sides are equal.

Hence, since neither of the conditions is satisfied by the information given, it follows that Choice D is correct.

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Find the area of a triangle whose vertices have the coordinates (-1,1) (-1,5) (4,1)

Alekssandra [29.7K]

The triangle that forms is a right-angled triangle. To work out the area, you just do the base × height, all divided by 2.

Therefore, you do 5 (the base) × 4 (the height) and you get 20.

Then you divide by 2 to finish the equation and you should find that the total area of the triangle is 10 units² (20 ÷ 2 = 10).

Hope that helps :)

7 0

3 years ago

PLEASE WILL GIVE 50 POINTS PLEASE ANSWER

leva [86]

Answer:

AB = 75

BC = 60

AC = 45

m∠A = 53°

m∠B = 37°

m∠C = 90°

Step-by-step explanation:

<u>Trigonometric ratios</u>

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle
H is the hypotenuse (the side opposite the right angle)

Given:

$\sf \tan(A)=\dfrac{60}{45}$

Therefore:

side opposite angle A = BC = 60
side adjacent angle A = AC = 45

To find the length of AB (the hypotenuse), use Pythagoras’ Theorem:

$a^2+b^2=c^2$

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

⇒ AC² + BC² = AB²

⇒ 45² + 60² = AB²

⇒ AB² = 5625

⇒ AB = √5625

⇒ AB = 75

To find m∠A:

$\implies\sf \tan(A)=\dfrac{60}{45}$

$\implies\sf A=\tan^{-1}\left(\dfrac{60}{45}\right)$

$\implies\sf A=53^{\circ}\:(nearest\:degree)$

m∠C = 90° (as it is a right angle)

The interior angles of a triangle sum to 180°

⇒ m∠A + m∠B + m∠C = 180°

⇒ 53° + m∠B + 90° = 180°

⇒ m∠B = 180° - 53° - 90°

⇒ m∠B = 37°

4 0

2 years ago

How to put percent into decimal

fiasKO [112]

Answer:

There are multiple ways to do so:

You can divide the number by 100 to convert it to a decimal

You could take your percentage and add a decimal two places to the left.

Examples of both:

For division its as simple as 75 divided by 100 = 0.75

If we are going to use the decimal method, lets say we have 45%, so we can do this:

45% =45.00

Move the decimal two places to the left.

0.45

6 0

3 years ago

A news report says that 9% of middle school students are on the track team.

Ratling [72]

Answer:

54 students.

Step-by-step explanation:

If you have 600 and 9% the nearest rounding point is %10. %10 of 600 is 60, and 1% of 60 is 6, so 60-6=54.

3 0

3 years ago

To get to school you can travel by car, bus or bicycle. If you travel by car, there is a 50% chance you will be late because the

Irina18 [472]

Answer:

a) 16.66%

b) 5%

Step-by-step explanation:

Since the teacher assumes each of the three possibilities are equally likely, then he assumes 33.33% to each one.

In this case the probability that you traveled to school that day by car would be

50% of 33.33% = (0.5)(0.3333) = 0.1666 = 16.66%

In this case, the teacher would assume

90% ride on bicycle

0% take the bus

10% travel by car

So, in this case the probability would be

50% of 10% = (0.5)(0.1) = 0.05 = 5%

6 0

3 years ago