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2 years ago

Given: △RST ~ △VWX

Mathematics

1 answer:

tatiyna2 years ago

4 0

Answer:

Given

Step-by-step explanation:

Given that: △RST ~ △VWX, TU is the altitude of △RST, and XY is the altitude of △VWX.

Comparing △RST and △VWX;

TU ~ XY (given altitudes of the triangles)

<TUS = <XYW (all right angles are congruent)

<UTS ≅ <YXW (angle property of similar triangles)

Thus;

ΔTUS ≅ ΔXYW (congruent property of similar triangles)

<UTS + <TUS + < UST = <YXW + <XTW + <XWY = $180^{0}$ (sum of angles in a triangle)

Therefore by Angle-Angle-Side (AAS), △RST ~ △VWX

So that:

$\frac{TU}{XY}$ = $\frac{US}{YW}$ (corresponding side length proportion)

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pshichka [43]

As shown in the figure

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∵ ∠B= ∠D=90°

∠C is common.

So by AA similarity ΔABC and ΔEDC are similar.

As we know when triangles are similar their sides are proportional.

AB/AD =BC/DC

Let DC=x meter

⇒ $\frac{10}{x}=\frac{30+x}{x}$

⇒5=\frac{30+x}{x}[/tex]

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2 years ago

Please help me out with this

UNO [17]

Step-by-step explanation:

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2 years ago

Prove :<br>sin²θ + cos²θ = 1<br><br><br>thankyou ~

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Answer:

See below

Step-by-step explanation:

Here we need to prove that ,

$\sf\longrightarrow sin^2\theta + cos^2\theta = 1$

Imagine a right angled triangle with one of its acute angle as $\theta$ .

The side opposite to this angle will be perpendicular .
Also we know that ,

$\sf\longrightarrow sin\theta =\dfrac{p}{h} \\$

$\sf\longrightarrow cos\theta =\dfrac{b}{h}$

And by Pythagoras theorem ,

$\sf\longrightarrow h^2 = p^2+b^2 \dots (i)$

Where the symbols have their usual meaning.

Now , taking LHS ,

$\sf\longrightarrow sin^2\theta +cos^2\theta$

Substituting the respective values,

$\sf\longrightarrow \bigg(\dfrac{p}{h}\bigg)^2+\bigg(\dfrac{b}{h}\bigg)^2\\$

$\sf\longrightarrow \dfrac{p^2}{h^2}+\dfrac{b^2}{h^2}\\$

$\sf\longrightarrow \dfrac{p^2+b^2}{h^2}$

From equation (i) ,

$\sf\longrightarrow\cancel{ \dfrac{h^2}{h^2}}\\$

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Since LHS = RHS ,

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1 year ago

Four more than twice a number is -10.

Vadim26 [7]

Answer:

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Step-by-step explanation:

Check work:

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3 years ago

Read 2 more answers

Ms. Hagan invested twice as much money in an account that pays 7% interest as she did in an account that pays 6% in interest. He

Karo-lina-s [1.5K]

Answer: She invested $5000 in an account that pays 6% interest and $10000 in an account that pays 7% interest.

Step-by-step explanation:

Let P be the initial amount she invested in an account that pays 6% interest.

Then, amount invested in other account = 2P

Simple interest = Principal x rate x time

After one year, for the first account,

Interest = P(0.06)(1) = 0.06P

For second account,

Interest = (2P)(0.07)(1)=0.14P

Total interest = $0.06P+0.14P=1000$

$\Rightarrow\ 0.20P=1000\\\\\Rightarrow\ P=\dfrac{1000}{0.20}\\\\\Rightarrow\ P=5000$

2P = 2(5000)=10000

Hence, She invested $5000 in an account that pays 6% interest and $10000 in an account that pays 7% interest.

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2 years ago