Question

soup
directions: define the following vocabulary

1. hypotenuse:
2. opposite side:
3. adjacent side:

house salad
directions: complete all tasks below using trig functions.
θ = angle (theta)

1. fill in the blanks below to complete the three trigonometric ratios.
2. use your calculator to find the sine, cosine, and tangent of each acute angle in the triangle below.

(write the first 3 decimal places)
measure of angle | sine ($\frac{opp}{hyp}$) | cosine ($\frac{adj}{hyp}$) | tangent ($\frac{opp}{adj}$)
30° | | |
60° | | |

Explanation:

Step1: Define trigonometry terms

Hypotenuse:

The longest side of a right triangle, opposite the right angle.

Opposite side:

The side across from a given acute angle in a right triangle.

Adjacent side:

The side next to a given acute angle (not the hypotenuse) in a right triangle.

Step2: Fill trigonometric ratios

$\sin\theta = \frac{\text{Opposite}}{\text{Hypotenuse}}$
$\cos\theta = \frac{\text{Adjacent}}{\text{Hypotenuse}}$
$\tan\theta = \frac{\text{Opposite}}{\text{Adjacent}}$

Step3: Calculate trig values for 30°

Use calculator (ensure degree mode):
$\sin(30^\circ) = 0.500$
$\cos(30^\circ) \approx 0.866$
$\tan(30^\circ) \approx 0.577$

Step4: Calculate trig values for 60°

Use calculator (ensure degree mode):
$\sin(60^\circ) \approx 0.866$
$\cos(60^\circ) = 0.500$
$\tan(60^\circ) \approx 1.732$

Answer:

Soup Section:

1. Hypotenuse: The longest side of a right triangle, opposite the right angle.
2. Opposite side: The side across from a given acute angle in a right triangle.
3. Adjacent Side: The side next to a given acute angle (not the hypotenuse) in a right triangle.

House Salad Section:

1. Trigonometric ratios:

$\sin\theta = \frac{\text{Opposite}}{\text{Hypotenuse}}$, $\cos\theta = \frac{\text{Adjacent}}{\text{Hypotenuse}}$, $\tan\theta = \frac{\text{Opposite}}{\text{Adjacent}}$

1. Trigonometric values table:

Measure of Angle	Sine	Cosine	Tangent
60°	0.866	0.500	1.732