Question

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Answer 1

Answer:

Step-by-step explanation:

a). Since, ΔABC ~ ΔWYZ

Their corresponding sides will be proportional.

$\frac{AB}{WY}=\frac{BC}{YZ}= \frac{AC}{WZ}$

$\frac{194}{WY}=\frac{BC}{1}= \frac{130}{WZ}$  --------(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)

$\frac{194}{WY}=\frac{144}{1}= \frac{130}{WZ}$

$\frac{194}{WY}=\frac{144}{1}$

WY = $\frac{194}{144}$

WY = $\frac{97}{72}$ = 1.35

$\frac{144}{1}= \frac{130}{WZ}$

WZ = $\frac{130}{144}$

WZ = $\frac{65}{72}$ = 0.90

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

               = $\frac{144}{130}$

               = $\frac{72}{65}$

Since, ΔABC ~ ΔWYZ,

∠A ≅ ∠W

Therefore, tangent of angle A and angle W will measure $\frac{72}{65}$.