Question

5 practice 5 (from unit 4, lesson 4)
approximate the angles that have the following quotients. round your answers to the nearest degree.
a. adjacent leg \\( \div \\) hypotenuse = 0.966
type your answers in the boxes:

b. opposite leg \\( \div \\) hypotenuse = 0.469

c. adjacent leg \\( \div \\) hypotenuse = 0.309

d. opposite leg \\( \div \\) adjacent leg = 1.036

how did i do?

Explanation:

Part a

Step1: Recall cosine definition

Adjacent/hypotenuse is cosine, so we need to find $\theta$ where $\cos\theta = 0.966$.

Step2: Use inverse cosine

$\theta=\cos^{-1}(0.966)$. Calculate this using a calculator (in degree mode). $\cos^{-1}(0.966)\approx15^\circ$.

Part b

Step1: Recall sine definition

Opposite/hypotenuse is sine, so we need to find $\theta$ where $\sin\theta = 0.469$.

Step2: Use inverse sine

$\theta=\sin^{-1}(0.469)$. Calculate this using a calculator (in degree mode). $\sin^{-1}(0.469)\approx28^\circ$.

Part c

Step1: Recall cosine definition

Adjacent/hypotenuse is cosine, so we need to find $\theta$ where $\cos\theta = 0.309$.

Step2: Use inverse cosine

$\theta=\cos^{-1}(0.309)$. Calculate this using a calculator (in degree mode). $\cos^{-1}(0.309)\approx72^\circ$.

Part d

Answer:

s:
a. $\boldsymbol{15^\circ}$
b. $\boldsymbol{28^\circ}$
c. $\boldsymbol{72^\circ}$
d. $\boldsymbol{46^\circ}$