Answer:
Step-by-step explanation:
a). Since, ΔABC ~ ΔWYZ
Their corresponding sides will be proportional.
[tex]\frac{AB}{WY}=\frac{BC}{YZ}= \frac{AC}{WZ}[/tex]
[tex]\frac{194}{WY}=\frac{BC}{1}= \frac{130}{WZ}[/tex] --------(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)
[tex]\frac{194}{WY}=\frac{144}{1}= \frac{130}{WZ}[/tex]
[tex]\frac{194}{WY}=\frac{144}{1}[/tex]
WY = [tex]\frac{194}{144}[/tex]
WY = [tex]\frac{97}{72}[/tex] = 1.35
[tex]\frac{144}{1}= \frac{130}{WZ}[/tex]
WZ = [tex]\frac{130}{144}[/tex]
WZ = [tex]\frac{65}{72}[/tex] = 0.90
b). tan(A) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{144}{130}[/tex]
= [tex]\frac{72}{65}[/tex]
Since, ΔABC ~ ΔWYZ,
∠A ≅ ∠W
Therefore, tangent of angle A and angle W will measure [tex]\frac{72}{65}[/tex].
