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2 years ago

Trigonometry: Angles and Length Escape Room (level 3)

Mathematics

1 answer:

Andre45 [30]2 years ago

6 0

Answer:

A -) E -) I -) F -) C -) H -) K -) Escape!

Step-by-step explanation:

I calculated it, so shouldn't be wrong but tell me if it is.

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SIMPLIFY THEN ADD 4 TO SUBBTRACT 5

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3 years ago

Calculate the volume of each pyramid to determine

kipiarov [429]

Answer:

1: 120

2: 138

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Step-by-step explanation:

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3 years ago

PLEASE HELP: For the next RSM Award ceremony, it was decided to decrease the length of the main poster by 12% and to increase i

MrRissso [65]

Let me set an example to help solve this, say the poster is 100 inches by 90 inches. the length of the poster is reduced by 12% so subtract 12 from 100 to get you new length of 78 inches. the width is increased by 15% so multiply 90 by 15% to get 13.5 inches and add the to the 90 inches you have to get your new width of 103.5 inches. multiply them together to get your new area then divide the new area by the old area, subtract that number by 1 and multiply it by -1.

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2 years ago

Pls help will give brainiest. Find the length of side A.

Drupady [299]

I think the answer is 12.

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3 years ago

The figure below shows two triangles EFG and KLM.

grandymaker [24]

A right triangle is a triangle that has a right angle of 90 degrees. In this exercise, we have two of this type of triangles. To solve this problem, we will apply some properties of triangles, so:

1. Which step can be used to prove that triangle EFG is also a right triangle?

To prove this, we need to use Pythagorean Theorem. So, for triangle EGF, if the formula:

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

is true, then EFG is also a right triangle. The steps are:

Square a

Square b

Square c

If the sum of the square of a and the sum of the square of b equals the square of c, then this is a right triangle.

2. Prove that the sum of a and c is greater than b.

We need to prove that:

$a+c>b$

From trigonometry, we know that:

$a=c \times sin(\theta) \\ \\ b=c \times cos(\theta) \\ \\ where \ \theta=\angle EFG \\ \\$

By substituting these values in the previous inequality:

$c \times sin(\theta)+c>c \times cos(\theta) \\ \\ Since \ c>0 \\ \\ sin(\theta)+1>cos(\theta) \\ \\ 1>cos(\theta)-sin(\theta)$

Since $\theta$ is an angle greater than 0 and less than 90 degrees, $cos(\theta) \ and \ sin(\theta)$ are numbers between 0 (greater than) and 1. Therefore, this inequality is always true. So, the statement has been proved.

3. Prove that the sum of a and b is greater than c.

We need to prove that:

$a+b>c$

Applying the same reasoning as in 2:

$c \times sin(\theta)+c \times cos(\theta)>c \\ \\ Since \ c>0 \\ \\ sin(\theta)+cos(\theta)>1$

This inequality is always true. So, the statement has been proved.

4. Prove that triangles are congruent by SSS property and hence angle EGF is equal to angle KML.

SSS means that we know the three sides of the triangle and want to find the missing angles. For ΔEGF, we know the three sides, and for KML, since this is a right triangle KL = c, therefore the corresponding sides of these two triangles are equal. Accordingly, these two triangles are congruent by SSS and angle EGF is equal to angle KML.

5. Prove that the ratio of EF and KL is greater than 1 and hence the triangles are similar by AA postulate.

The ratio of EF and KL is:

$\frac{EF}{KL}$

The statement is true if and only if EF > KL. Then, according to AA postulate, two triangles are similar if they have two corresponding angles congruent. So:

EGF is congruent to KML and equals 90 degrees
GEF is congruent to MKL
EFG is conguent to KLM

Accordingly, the triangles are similar.

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3 years ago

Read 2 more answers