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3 years ago

What is the length of the diagonal of the rectangle? Round to two decimal places

Mathematics

1 answer:

yan [13]3 years ago

3 0

Answer:

Option C

Step-by-step explanation:

By the property of a rectangle,

"All interior angles of a rectangle measure 90°"

Therefore, m∠ABC = 90°

By applying cosine rule in the right triangle ABC,

cos(∠CAB) = $\frac{\text{Adjacent side}}{\text{Hypotenuse}}$

cos(25°) = $\frac{AB}{AC}$

AC = $\frac{AB}{\text{cos}(25)}$

AC = $\frac{18}{\text{cos}(25)}$

AC = 19.86

Therefore, Option C will be the answer.

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3 years ago

Right triangles abc and dbc with right angle c are given below. If cos(a)=15,ab=12 and cd=2, find the length of bd.

dmitriy555 [2]

see the attached figure to better understand the problem

we have that

$cos(A)=\frac{1}{5} \\ AB=12\ units\\ CD=2\ units$

Step 1

Find the value of AC

we know that

in the right triangle ABC

$cos (A)=(AC/AB)\\AC=AB*cos(A)$

substitute the values in the formula

$AC=12*(1/5)\\ AC=2.4\ units$

Step 2

Find the value of BC

we know that

in the right triangle ABC

Applying the Pythagorean Theorem

$AB^{2} =AC^{2}+BC^{2}\\ BC^{2}=AB^{2} -AC^{2}$

substitute the values

$BC^{2}=12^{2} -2.4^{2}\\BC^{2}= 138.24\\ BC=11.76\ units$

Step 3

Find the value of BD

we know that

in the right triangle BCD

Applying the Pythagorean Theorem

$BD^{2} =DC^{2}+BC^{2}$

substitute the values

$BD^{2} =2^{2}+11.76^{2}$

$BD=11.93\ units$

therefore

the answer is

the length of BD is 11.93 units

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3 years ago

Read 2 more answers

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geniusboy [140]

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3 years ago

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yKpoI14uk [10]

Answer:

The graph in the attached figure N 2

Step-by-step explanation:

The complete question in the attached figure N 1

we have the ordered pairs

(-4,9),(-1,3),(0,1),(2,-3)

Using a graphing tool

Plot the given ordered pairs in the coordinate plane

Remember that

In a ordered pair (x,y), the first coordinate is the location of the point in the x-axis and the second coordinate is the location of the point in the y-axis

see the attached figure

The graph represent a line

Find the equation of the line

Find the slope

take two points

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