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3 years ago

The image below shows one of the walls of a house in the shape of a trapezoid. What is the total area of the wall?

Mathematics

2 answers:

Doss [256]3 years ago

5 0

I believe the answer to your question will be C. Hope this helps :)

QveST [7]3 years ago

4 0

I don’t know but I believe that it is c. 97.2

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Suppose that θ is an acute angle of a right triangle and that sec(θ)=52. Find cos(θ) and csc(θ).

insens350 [35]

Answer:

$\cos{\theta} = \dfrac{1}{52}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

Step-by-step explanation:

To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.

a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:

$\sec{\theta} = \dfrac{1}{\cos{\theta}}$

we can substitute the value of sec(θ) in this equation:

$52 = \dfrac{1}{\cos{\theta}}$

and solve for for cos(θ)

$\cos{\theta} = \dfrac{1}{52}$

side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by $\theta = \arccos{\left(\dfrac{1}{52}\right)} = 88.8^\circ$

b) since right triangle is mentioned in the question. We can use:

$\cos{\theta} = \dfrac{\text{adj}}{\text{hyp}}$

we know the value of cos(θ)=1\52. and by comparing the two. we can say that:

length of the adjacent side = 1
length of the hypotenuse = 52

we can find the third side using the Pythagoras theorem.

$(\text{hyp})^2=(\text{adj})^2+(\text{opp})^2$

$(52)^2=(1)^2+(\text{opp})^2$

$\text{opp}=\sqrt{(52)^2-1}$

$\text{opp}=\sqrt{2703}$

length of the opposite side = √(2703) ≈ 51.9904

we can find the sin(θ) using this side:

$\sin{\theta} = \dfrac{\text{opp}}{\text{hyp}}$

$\sin{\theta} = \dfrac{\sqrt{2703}}{52}}$

and since $\csc{\theta} = \dfrac{1}{\sin{\theta}}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

4 0

3 years ago

Antonio finds a pair of skis that cost $350 before tax. Sales tax is 6%. What is the total cost Antonio will have to pay for the

Ksju [112]

Answer:

$371

Step-by-step explanation:

5 0

4 years ago

Can anyone please help me with this ?

djverab [1.8K]

Answer:

The distance from point A to the top of the building is 5 $\sqrt{2}$ feet

The Height of the Skyscraper is 5 feet

Step-by-step explanation:

Given

Let Top point of building be point C

Also Let Base of the building be point B

Distance from point A to base B of the building AB= 5 feet

∴ It makes a Right angle triangle

Also ∠ACB = 45°

Also tan 45° = 1

Now tan ∠ACB = $\frac{AB}{BC}$

∴ AB= BC =5 feet

The Height of the Skyscraper is 5 feet

Now Triangle ABC is right angle triangle with right angled at B

So by Pythagoras theorem

AC= $\sqrt{AB^2+BC^2}=\sqrt{5^2+5^2} =\sqrt{50} =\sqrt{25\times2} =\sqrt{5^2\times2}=5\sqrt{2}$

The distance from point A to the top of the building is 5 $\sqrt{2}$ feet

5 0

3 years ago

Read 2 more answers

If the smaller of two numbers is one-half of the larger number and the sum of the two numbers is 81 , find the numbers.

zavuch27 [327]

Let smaller number be x/2 and the larger number x.

x/2 + x = 81
x/2 + x = 3x/2
3x/2 = 81
3x = 162
x= 54

The smaller number is 54/2= 27 and the larger number is 54.

4 0

2 years ago

What is greater 2yards or5feet

Brilliant_brown [7]

yards, there are 3 feet per yard

7 0

3 years ago

Read 2 more answers