Describe three ways to determine the measure of segment yz

Asked by maham237 @ 20/05/2021 in Mathematics viewed by 481 People

Answered by maham237 @ 20/05/2021

(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:
$\frac{50}{sin(90)} = \frac{YZ}{sin(30)}$
$50 = \frac{YZ}{sin(30)}$
$50sin(30) = YZ$
$YZ = 25$

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