Question

modern algebra 2 unit 1 review day 1 name:may ado determine which trig function is appropriate for the diagram. 1) 2) 3) 4) solve for the missing angle measure - round each answer to the nearest hundredth. 5) 6) 7) 8)

Explanation:

Step1: Recall trig - function definitions

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Analyze problem 5

In right - triangle 5, for angle $\theta$, the opposite side $BC = 10$ and the hypotenuse $AB = 11$. So, $\sin\theta=\frac{10}{11}$. Then $\theta=\sin^{- 1}(\frac{10}{11})\approx65.38^{\circ}$.

Step3: Analyze problem 6

In right - triangle 6, for angle $\theta$, the adjacent side $BC = 5$ and the hypotenuse $AB=\sqrt{6.4^{2}+5^{2}}=\sqrt{40.96 + 25}=\sqrt{65.96}\approx8.12$. So, $\cos\theta=\frac{5}{\sqrt{65.96}}$. Then $\theta=\cos^{-1}(\frac{5}{\sqrt{65.96}})\approx51.32^{\circ}$.

Step4: Analyze problem 7

In right - triangle 7, for angle $\theta$, the adjacent side $BC = 14$ and the hypotenuse $AB = 16$. So, $\cos\theta=\frac{14}{16}=\frac{7}{8}$. Then $\theta=\cos^{-1}(\frac{7}{8})\approx28.96^{\circ}$.

Step5: Analyze problem 8

In right - triangle 8, for angle $\theta$, the opposite side $BC = 7$ and the hypotenuse $AB = 11$. So, $\sin\theta=\frac{7}{11}$. Then $\theta=\sin^{-1}(\frac{7}{11})\approx39.54^{\circ}$.

Answer:

1. $\theta\approx65.38^{\circ}$
2. $\theta\approx51.32^{\circ}$
3. $\theta\approx28.96^{\circ}$
4. $\theta\approx39.54^{\circ}$