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3 years ago

Triangle OPQ is similar to triangle RST. Find the measure of side RS. Round your answer to the nearest tenth if necessary. OPQR

Mathematics

1 answer:

Andrews [41]3 years ago

3 0

Answer:

RS = 75.3

Step-by-step explanation:

You need to set up the proportion of corresponding sides.

$\frac{PQ}{ST} = \frac{PO}{RS}$

$\frac{7}{31} = \frac{17}{RS}$

7(RS) = 31(17)

= 527

RS = 527/7 = 75.2857...

= 75.3

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vredina [299]

Answer:

$x = 49.8^\circ\\y = 54.6^\circ$

Step-by-step explanation:

Kindly refer to the image attached in the answer region for labeling of triangle.

AB = 16

BC = 19

AC = 15

$\angle ABC = x^\circ\\\angle ACB = y^\circ$

We have to find the angles x and y i.e. $\angle B \text{ and }\angle C$ .

Formula for cosine rule:

$cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}$

Where

a is the side opposite to $\angle A$ ,

b is the side opposite to $\angle B$ and

c is the side opposite to $\angle C$ .

$\Rightarrow cos x = \dfrac{19^{2}+16^{2}-15^{2}}{2 \times 19 \times 16}\\\Rightarrow cos x = \dfrac{392}{608} \\\Rightarrow x = 49.8^\circ$

Similarly, for finding the value of y:

$cos C = \dfrac{a^{2}+b^{2}-c^{2}}{2ab}\\\Rightarrow cos y = \dfrac{19^{2}+15^{2}-16^{2}}{2 \times 19 \times 15}\\\Rightarrow cos y = \dfrac{330}{570}\\\Rightarrow y = 54.6^\circ$

Hence, the values are:

$x = 49.8^\circ\\y = 54.6^\circ$

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3 years ago

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erastovalidia [21]

Answer:

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Step-by-step explanation:

we know that

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shtirl [24]

Answer:

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