Question

This is pre calculus please help !Describe three ways to determine the measure of segment YZ.

Answer 1

(1) Using trigonometric ratios:
$sin(30) = \frac{YZ}{50}$
$YZ = 25$

(2) Using Pythagoras' Theorem:
$cos(30) = \frac{XY}{50}$
$50cos(30) = XY$
$50^{2} - 50^{2}cos^{2}(30) = YZ^{2}$
$2500 - 2500cos^{2}(30) = YZ^{2}$
$YZ = 25$

(3) Using sine rule:
$\frac{50}{sin(90)} = \frac{YZ}{sin(30)}$
$50 = \frac{YZ}{sin(30)}$
$50sin(30) = YZ$
$YZ = 25$

Answer 2

The method that can be used to measure the segment will be:

• Using trigonometric ratios.
• Using Pythagoras Theorem.
• Using sine rule.

It should be noted that when they trigonometric rule is used, YZ will be:

= Sin 30 × 50

= 25

Also, the Pythagoras Theorem and using sine rule gives the value of 25.

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