Question

1. find the missing angle: (tan)

a) 56.3 b) 33.7
c) 48.2 d) 41.8

1. find the missing angle: (tan)

a) 53.7 b) 36.3
c) 42.8 d) 47.2

1. find the missing angle: (tan)

Explanation:

Step1: Recall the tangent formula

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).

Step2: Solve for the first problem (angle \(A\) or \(C\))

Assume we want to find angle \(C\) in the first triangle (\(AB = 20\), \(BC=30\)). Using \(\tan C=\frac{AB}{BC}\), so \(\tan C=\frac{20}{30}=\frac{2}{3}\). Then \(C=\arctan(\frac{2}{3})\approx33.7^{\circ}\).

Step3: Solve for the second problem (angle \(A\))

In the second triangle (\(AB = 11\), \(BC = 15\)), \(\tan A=\frac{BC}{AB}\). So \(\tan A=\frac{15}{11}\), and \(A=\arctan(\frac{15}{11})\approx53.7^{\circ}\).

Step4: Solve for the third problem (angle \(C\))

In the third triangle (\(AB = 11\), \(BC = 15\)), \(\tan C=\frac{AB}{BC}\). So \(\tan C=\frac{11}{15}\), and \(C=\arctan(\frac{11}{15})\approx36.3^{\circ}\) (assuming the problem is similar to the first two, using the right - triangle tangent relationship).

Answer:

1. B. \(33.7\)
2. A. \(53.7\)
3. B. \(36.3\)