Question

1. use the triangle below to write each trig ratio. then find the measure of angle a. reduce your fractions.

a. sin(a) =
b. cos(a) =
c. tan(a)=
d. m∠a =
for problems #11 - 14, solve for x using right - triangle trigonometry. show all work to receive full or partial credit! round all answers to the hundredths.

1. x =
2. x =
3. x =
4. x =

Explanation:

Step1: Recall trig - ratio definitions

In a right - triangle, $\sin(A)=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos(A)=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan(A)=\frac{\text{opposite}}{\text{adjacent}}$. For right - triangle $ABC$ with $\angle B = 90^{\circ}$, opposite side to $\angle A$ is $BC = 30$, adjacent side to $\angle A$ is $AB = 16$, and hypotenuse $AC = 34$.

Step2: Calculate $\sin(A)$

$\sin(A)=\frac{BC}{AC}=\frac{30}{34}=\frac{15}{17}$

Step3: Calculate $\cos(A)$

$\cos(A)=\frac{AB}{AC}=\frac{16}{34}=\frac{8}{17}$

Step4: Calculate $\tan(A)$

$\tan(A)=\frac{BC}{AB}=\frac{30}{16}=\frac{15}{8}$

Step5: Calculate $m\angle A$

$m\angle A=\sin^{- 1}(\frac{15}{17})\approx61.93^{\circ}$

For problem 11:

Step1: Use tangent function

We know that $\tan(x)=\frac{12}{18}=\frac{2}{3}$. Then $x = \tan^{-1}(\frac{2}{3})\approx33.69^{\circ}$

For problem 12:

Step1: Use sine function

We know that $\sin(31^{\circ})=\frac{x}{5}$, so $x = 5\times\sin(31^{\circ})\approx5\times0.5150 = 2.58$

For problem 13:

Step1: Use tangent function

We know that $\tan(31^{\circ})=\frac{x}{13}$, so $x = 13\times\tan(31^{\circ})\approx13\times0.6009 = 7.81$

For problem 14:

Step1: Use tangent function

We know that $\tan(73^{\circ})=\frac{19}{x}$, so $x=\frac{19}{\tan(73^{\circ})}\approx\frac{19}{3.2709}\approx5.81$

Answer:

A. $\frac{15}{17}$
B. $\frac{8}{17}$
C. $\frac{15}{8}$
D. $61.93^{\circ}$

1. $33.69^{\circ}$
2. $2.58$
3. $7.81$
4. $5.81$