Given right triangle XYZ, what is the value of tan(Y)? One-half

StartFraction StartRoot 3 EndRoot Over 3 EndFraction

StartFraction StartRoot 3 EndRoot Over 2 EndFraction

StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction

Step-by-step explanation:

Find the diagram attached.

From the right triangle XYZ:

XY is the hypotenuse

XZ and YZ are opposite and adjacent

To get value of tan(Y), we will use the SOH, CAH, TOA, trigonometry identity.

According to TOA:

Tan(Y) = XZ/ZY

First let us get XZ

Using SOH

SinY = opp/hyp = XZ/XY

SinY = XZ/4

Sin30 = XZ/4

XZ = 4sin30

XZ = 4(0.5)

XZ = 2units

Next is to get ZY:

Using Pythagoras theorem:

ZY²+XZ² = XY²

ZY² = XY²-XZ²

ZY² = 4²-2²

ZY²  = 16-4

ZY²  = 12

ZY = √12

ZY = √4*3

ZY = 2√3

Solve for tan(Y):

Since Tan(Y) = XZ/ZY

Tan(Y) = 2/2√3

Tan(Y) = 1/√3

Rationalize

Tan(Y) = 1/√3*√3/√3

Tan(Y) = √3/√9

Tan(Y) = √3/3

Hence the correct option is A. StartFraction StartRoot 3 EndRoot Over 3 EndFraction

d. it is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

step-by-step explanation:

total amount to be paid = $19.5

step-by-step explanation:

given ,

original price = $25.99

discount = 25%

discount amount = 25% of original price

discount amount = 25/100   * 25.99

discount amount = $6.49

hence , the total amount to be paid = original price - discount amount

                                                            = $25.99 - $6.49

                                                            =$19.5

total amount to be paid = $19.5