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

Which did you include in your response?

Solve the equation where the sine of 30 degrees is equal to YZ/50.

Solve the equation where the tangent of 30 degrees is equal to YZ/50.

Solve 180 - (30 + 90) = 60 to find the measure of angle Z. Then use the cosine of Z to write and solve an equation.

Use the 30°-60°-90° triangle theorem to find that YZ = 50/2.