Question

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Answer 1

Explanation:

a). Since, ΔABC ~ ΔWYZ

Their corresponding sides will be proportional.

`(AB)/(WY)=(BC)/(YZ)= (AC)/(WZ)`

`(194)/(WY)=(BC)/(1)= (130)/(WZ)` --------(1)

By applying Pythagoras theorem in ΔABC,

AB² = AC² + BC²

BC² = AB² - AC²

BC² = (194)² - (130)²

BC² = 20736

BC = 144

From equation (1)

`(194)/(WY)=(144)/(1)= (130)/(WZ)`

`(194)/(WY)=(144)/(1)`

WY =
`(194)/(144)`

WY =
`(97)/(72)` = 1.35

`(144)/(1)= (130)/(WZ)`

WZ =
`(130)/(144)`

WZ =
`(65)/(72)` = 0.90

b). tan(A) =
`\frac{\text{Opposite side}}{\text{Adjacent side}}`

=
`(144)/(130)`

=
`(72)/(65)`

Since, ΔABC ~ ΔWYZ,

∠A ≅ ∠W

Therefore, tangent of angle A and angle W will measure
`(72)/(65)`.