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andrew11 [14]
3 years ago
14

A rectangle is to be inscribed in a right triangle having sides of length 6 in, 8 in, and 10 in. Find the dimensions of the rect

angle with greatest area assuming the rectangle is positioned as in Figure 1. Figure1

Mathematics
1 answer:
Helga [31]3 years ago
8 0

Answer:  width = 2.4 in, length = 5

<u>Step-by-step explanation:</u>

The max area of a right triangle is half the area of the original triangle.

Area of the triangle = (6 x 8)/2  = 24

--> area of rectangle = 24 ÷ 2 = 12

Next, let's find the dimensions.

The length is adjacent to the hypotenuse. Since we know the area is half, we should also know that the length will be half of the hypotenuse.

length = 10 ÷ 2 = 5

Use the area formula to find the width:

A = length x width

12 = 5 w

12/5 = w

2.4 = w

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Find the exact value by using a half-angle identity. sin(5pi/12)
anzhelika [568]

Find <span>tan<span>(<span><span>5π</span>12</span>)</span></span> and sin ((5pi)/12)
Answer: <span>±<span>(2±<span>√3</span>)</span>and±<span><span>√<span>2+<span>√3</span></span></span>2</span></span>

Explanation:

Call tan ((5pi/12) = t. 
Use trig identity: <span><span>tan2</span>a=<span><span>2<span>tana</span></span><span>1−<span><span>tan2</span>a</span></span></span></span>
<span><span>tan<span>(<span><span>10π</span>12</span>)</span></span>=<span>tan<span>(<span><span>5π</span>6</span>)</span></span>=−<span>1<span>√3</span></span>=<span><span>2t</span><span>1−<span>t2</span></span></span></span>
<span><span>t2</span>−2<span>√3</span>t−1=0</span>

<span>D=<span>d2</span>=<span>b2</span>−4ac=12+4=16</span>--> <span>d=±4</span>

<span>t=<span>tan<span>(<span><span>5π</span>12</span>)</span></span>=<span><span>2<span>√3</span></span>2</span>±<span>42</span>=2±<span>√3</span></span>

Call <span><span>sin<span>(<span><span>5π</span>12</span>)</span></span>=<span>siny</span></span>
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5 0
3 years ago
What is the distance between (–9,-6) and (-2,-2)?
Rufina [12.5K]

Answer:

8.0623

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Step-by-step explanation:

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3 years ago
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Can you please help me out
Taya2010 [7]

The bag contains,

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\text{Total marbles = (R) + (G) +(B) = 9 + 7 + 4 = 20 marbles}

Let P(R) represent the probablity of picking a red marble,

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P(B) represent the probability of picking a blue marble.

Probability , P, is,

\text{Prob, P =}\frac{required\text{ outcome}}{possible\text{ outcome}}\begin{gathered} P(R)=\frac{9}{20} \\ P(G)=\frac{7}{20} \\ P(B)=\frac{4}{20} \end{gathered}

Probablity of drawing a Red marble (R) and then a blue marble (B) without being replaced,

That means once a marble is drawn, the total marbles (possible outcome) reduces as well,

\begin{gathered} \text{Prob of a red marble P(R) =}\frac{9}{20} \\ \text{Prob of }a\text{ blue marble =}\frac{4}{19} \\ \text{After a marble is selected without replacement, marbles left is 19} \\ \text{Prob of red marble + prob of blue marble = P(R) + P(B) = }\frac{9}{20}+\frac{4}{19}=\frac{251}{380} \\ \text{Hence, the probability is }\frac{251}{380} \end{gathered}

Hence, the best option is G.

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1 year ago
Determine whether (18+35)x4=18 +35x4 is true or false. explain
Marizza181 [45]
False, because it would no longer be 18 alone because of the disturbutive property.
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3 years ago
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