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3 years ago

What is the measure of R?

Mathematics

2 answers:

tigry1 [53]3 years ago

8 0

Answer:

(D)68°

Step-by-step explanation:

Given: In ΔPQR, PQ=PR=5 and ∠PQR=68°.

To find: The measure of ∠R.

Solution:

From the given figure, it can be seen that both PQ and PR have the same measure that is 5 in length.

From the property of triangles that is if the two sides of triangle are equal, then the angles made by those sides are equal in measure.

Since, PQ and PR are equal, therefore ∠PQR=∠PRQ=68°.

Hence. the measure of the angle R is 68°.

Therefore, option D is correct.

Simora [160]3 years ago

5 0

The measure of R is the same as Q so the answer is 68 degrees

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16. Angle C is approximately 13.0 degrees.

17. The length of segment BC is approximately 45.0.

18. Angle B is approximately 26.0 degrees.

15. The length of segment DF "e" is approximately 12.9.

Step-by-step explanation:

By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.

For triangle ABC:

$\sin{A} = \sin{103\textdegree{}}$ ,
The opposite side of angle A $a = BC = 26$ ,
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Note that the inverse sine function here $\sin^{-1}()$ is also known as arcsin.

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$c^{2} = a^{2} + b^{2} - 2\;a\cdot b\cdot \cos{C}$ ,

where

$a$ , $b$ , and $c$ are the lengths of sides of triangle ABC, and
$\cos{C}$ is the cosine of angle C.

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$b = 21$ ,
$c = 30$ ,
The length of $a$ (segment BC) is to be found, and
The cosine of angle A is $\cos{123\textdegree}$ .

Therefore, replace C in the equation with A, and the law of cosine will become:

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$\displaystyle \begin{aligned}a &= \sqrt{b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}}\\&=\sqrt{21^{2} + 30^{2} - 2\times 21\times 30 \times \cos{123\textdegree}}\\&=45.0 \end{aligned}$ .

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$c = 6$ , and
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The length of segment DF is to be found,
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