Segment RS has endpoints at R(5,13). Point Q lies on line segment RS such that RQ : QS= 3:1. Which of the following must be the coordinates of Q?

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Ответ:

shayhiddinovxasan93

29.05.2020

Mathematics

Given:

In triangle $XYZ,m\angle X=90^\circ, m\angle Y=45^\circ, m\angle Z=45^\circ, XZ=y,YZ=15\sqrt{2}$ .

To find:

The value of y.

Solution:

In a right angle triangle,

$\sin \theta =\dfrac{Perpendicular}{Hypotenuse}$

Using the above ratio for the triangle XYZ, we get

$\sin Y =\dfrac{XZ}{YZ}$

$\sin 45^\circ =\dfrac{y}{15\sqrt{2}}$

$\dfrac{1}{\sqrt{2}}=\dfrac{y}{15\sqrt{2}}$

$\dfrac{15\sqrt{2}}{\sqrt{2}}=y$

15=y

Therefore, the correct option is C.

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