Question

2 practice 2 here is triangle abc. estimate the values to complete the table. round to the nearest hundredth if necessary. type your answers in the boxes. angle adjacent leg ÷ hypotenuse opposite leg ÷ hypotenuse opposite leg ÷ adjacent leg a c 0.97 0.26 0.27 how did i do?

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle \(ABC\) with right - angle at \(B\), for an angle \(\theta\), \(\cos\theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}\), \(\sin\theta=\frac{\text{opposite leg}}{\text{hypotenuse}}\), and \(\tan\theta=\frac{\text{opposite leg}}{\text{adjacent leg}}\). Also, for complementary angles \(A\) and \(C\) (\(A + C=90^{\circ}\)), \(\cos A=\sin C\), \(\sin A=\cos C\), and \(\tan A=\frac{1}{\tan C}\).

Step2: Calculate for angle \(A\)

• For \(\text{adjacent leg}\div\text{hypotenuse}\) (i.e., \(\cos A\)):

Since \(\cos A=\sin C\), and \(\sin C = 0.26\), so \(\cos A=0.26\).

• For \(\text{opposite leg}\div\text{hypotenuse}\) (i.e., \(\sin A\)):

Since \(\sin A=\cos C\), and \(\cos C = 0.97\), so \(\sin A=0.97\).

• For \(\text{opposite leg}\div\text{adjacent leg}\) (i.e., \(\tan A\)):

Since \(\tan A=\frac{1}{\tan C}\), and \(\tan C = 0.27\), so \(\tan A=\frac{1}{0.27}\approx3.70\).

Answer:

angle	adjacent leg ÷ hypotenuse	opposite leg ÷ hypotenuse	opposite leg ÷ adjacent leg