A person places $308 in an investment account earning an annual rate of 2.1%,

Work out the area of abcd.<br><br> please ensure you give workings out too.

ipn [44]

Answer:

$\displaystyle A_{\text{Total}}\approx45.0861\approx45.1$

Step-by-step explanation:

We can use the trigonometric formula for the area of a triangle:

$\displaystyle A=\frac{1}{2}ab\sin(C)$

Where a and b are the side lengths, and C is the angle <em>between</em> the two side lengths.

As demonstrated by the line, ABCD is the sum of the areas of two triangles: a right triangle ABD and a scalene triangle CDB.

We will determine the area of each triangle individually and then sum their values.

Right Triangle ABD:

We can use the above area formula if we know the angle between two sides.

Looking at our triangle, we know that ∠ADB is 55 DB is 10.

So, if we can find AD, we can apply the formula.

Notice that AD is the adjacent side to ∠ADB. Also, DB is the hypotenuse.

Since this is a right triangle, we can utilize the trig ratios.

In this case, we will use cosine. Remember that cosine is the ratio of the adjacent side to the hypotenuse.

Therefore:

$\displaystyle \cos(55)=\frac{AD}{10}$

Solve for AD:

$AD=10\cos(55)$

Now, we can use the formula. We have:

$\displaystyle A=\frac{1}{2}ab\sin(C)$

Substituting AD for a, 10 for b, and 55 for C, we get:

$\displaystyle A=\frac{1}{2}(10\cos(55))(10)\sin(55)$

Simplify. Therefore, the area of the right triangle is:

$A=50\cos(55)\sin(55)$

We will not evaluate this, as we do not want inaccuracies in our final answer.

Scalene Triangle CDB:

We will use the same tactic as above.

We see that if we can determine CD, we can use our area formula.

First, we can determine ∠C. Since the interior angles sum to 180 in a triangle, this means that:

$\begin{aligned}m \angle C+44+38&=180 \\m\angle C+82&=180 \\ m\angle C&=98\end{aligned}$

Notice that we know the angle opposite to CD.

And, ∠C is opposite to BD, which measures 10.

Therefore, we can use the Law of Sines to determine CD:

$\displaystyle \frac{\sin(A)}{a}=\frac{\sin(B)}{b}$

Where A and B are the angles opposite to its respective sides.

So, we can substitute 98 for A, 10 for a, 38 for B, and CD for b. Therefore:

$\displaystyle \frac{\sin(98)}{10}=\frac{\sin(38)}{CD}$

Solve for CD. Cross-multiply:

$CD\sin(98)=10\sin(38)$

Divide both sides by sin(98). Hence:

$\displaystyle CD=\frac{10\sin(38)}{\sin(98)}$

Therefore, we can now use our area formula:

$\displaystyle A=\frac{1}{2}ab\sin(C)$

We will substitute 10 for a, CD for b, and 44 for C. Hence:

$\displaystyle A=\frac{1}{2}(10)(\frac{10\sin(38)}{\sin(98)})\sin(44)$

Simplify. So, the area of the scalene triangle is:

$\displaystyle A=\frac{50\sin(38)\sin(44)}{\sin(98)}$

Therefore, our total area will be given by:

$\displaystyle A_{\text{Total}}=50\cos(55)\sin(55)+\frac{50\sin(38)\sin(44)}{\sin(98)}$

Approximate. Use a calculator. Thus:

$\displaystyle A_{\text{Total}}\approx45.0861\approx45.1$

8 0

3 years ago

Can someone help me with this? thx :)

GrogVix [38]

Answer:

Table 1 is not a function because there are two y-values with the same x-values. Remember... y values can repeat but x values cannot repeat when their corresponding y values are different.

Table 2 is a function.

You would need to omit either (3,7) or (3,-2).

Please vote brainliest! Hope this helps, have a nice day.

8 0

3 years ago

Read 2 more answers

Martha filled a bowl with 0.5 cup of flour and 0.75 cup of milk. To the nearest cup, how many cups of ingredients were in the bo

Damm [24]

0.5 + 0.75 = 1.25

1.25 rounds off to 1.

7 0

3 years ago

PLEASE HELP ill give brainlist to the first right answer

attashe74 [19]

Answer:

Step-by-step explanation:

Put it into y=mx+b form and use substitution.

3 0

3 years ago

PLEASE HELP WITH GEOMETRY IM STUCK!?}

Ilya [14]

Answer:

13.8

Step-by-step explanation:

Recall the trigonometric ratios

Sine = Opposite over Hypotenuse (SOH)

Cosine = Adjacent over Hypotenuse (CAH)

Tangent = Opposite over Adjacent (TOA)

Now lets look back at the question

We are given an angle and its adjacent side length (11) and we need to find the hypotenuse

The hypotenuse and adjacent sides corresponds with the trig function cosine so we will use cosine to solve for x

( remember that cosine = adjacent over hypotenuse )

$cos(37)=\frac{11}{x}$

step 1 multiply each side by x

$cos(37)*x=xcos(37)\\\frac{11}{x} *x=11$

now we have $xcos(37)=11$

step 2 divide each side by cos(37)

$\frac{xcos(37)}{cos(37)} =x\\\frac{11}{cos(37)} =13.77349\\$

we're left with x = 13.77439

Our last step would be to round to the nearest tenth

We would get that the answer is 13.8

3 0

2 years ago

Read 2 more answers