Question

17 solve for x using trig ratios (soh - cah - toa): a 20 cos(60)=10.00 b 20 sin(60)=17.32 c 20 tan(60)=34.64 18 solve for x using trig ratios (soh - cah - toa): a 14 sin(28)=6.57 b 14 cos(28)=12.36 c 14 tan(28)=7.44 19 tan(80)= a 3.27 b 5.67 c 7.43 d 8.13 20 sin(20)= a 0.34 b 0.89 c 3.27 d 8.13

Explanation:

Step1: Recall cosine ratio

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For the first triangle with hypotenuse $20$ and angle $60^{\circ}$, if $x$ is the adjacent side to the $60^{\circ}$ angle, then $x = 20\cos(60^{\circ})$. Since $\cos(60^{\circ})=\frac{1}{2}$, $x = 20\times\frac{1}{2}=10$. So the answer for question 17 is A.

Step2: Recall tangent ratio

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For the second triangle with adjacent side to the $28^{\circ}$ angle as $x$ and opposite side $14$, then $x=\frac{14}{\tan(28^{\circ})}$. Also, if we consider the relationship in terms of the given options, we know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$, so $x = 14\tan(28^{\circ})$. Using a calculator, $14\tan(28^{\circ})\approx7.44$. So the answer for question 18 is C.

Step3: Calculate tangent value

Using a scientific calculator, $\tan(80^{\circ})\approx5.67$. So the answer for question 19 is B.

Step4: Calculate sine value

Using a scientific calculator, $\sin(20^{\circ})\approx0.34$. So the answer for question 20 is A.

Answer:

1. A. $20\cos(60)=10.00$
2. C. $14\tan(28)=7.44$
3. B. $5.67$
4. A. $0.34$