Question

1. complete each trigonometric ratio below (think about soh-cah-toa).

a. sine =
b. cosine =
c. tangent =
find the indicated trigonometric ratio and write in simplest form.

1. sin a
2. sin b
3. cos a
4. cos x
5. tan z
6. tan b

find the indicated ratios. give your answer as a fraction in simplest form.
8.
missing side = ______
sin a = ____ cos a = __ tan a = ____
9.
missing side = ______
sin a = ____ cos a = __ tan a = ____

Explanation:

Step1: Identify trigonometric ratios (SOH-CAH-TOA)

Sine = Opposite/Hypotenuse; Cosine = Adjacent/Hypotenuse; Tangent = Opposite/Adjacent

Step2: Calculate Sin A (Q2)

For △ABC (∠C=90°), opposite to A is 21, hypotenuse 29 → $\frac{21}{29}$

Step3: Calculate Sin B (Q3)

For △ABC (∠C=90°), opposite to B is 35, hypotenuse 37 → $\frac{35}{37}$

Step4: Calculate Cos A (Q4)

For △ABC (∠C=90°), adjacent to A is 8, hypotenuse 17 → $\frac{8}{17}$

Step5: Calculate Cos X (Q5)

For △XYZ (∠Y=90°), adjacent to X is 21, hypotenuse 29 → $\frac{21}{29}$

Step6: Calculate Tan Z (Q6)

For △XYZ (∠Y=90°), opposite to Z is 32, adjacent 24 → $\frac{32}{24}=\frac{4}{3}$

Step7: Calculate Tan B (Q7)

For △ABC (∠C=90°), opposite to B is 18, adjacent 24 → $\frac{18}{24}=\frac{3}{4}$

Step8: Solve Q8 (△ABC, ∠C=90°, AB=15, BC=9)

Missing side AC: $AC=\sqrt{15^2-9^2}=12$; Sin A=9/15=3/5; Cos A=12/15=4/5; Tan A=9/12=3/4

Step9: Solve Q9 (△ABC, ∠C=90°, AC=6, AB=10)

Missing side BC: $BC=\sqrt{10^2-6^2}=8$; Sin A=8/10=4/5; Cos A=6/10=3/5; Tan A=8/6=4/3

Answer:

1a. Opposite/Hypotenuse
1b. Adjacent/Hypotenuse
1c. Opposite/Adjacent

1. $\frac{21}{29}$
2. $\frac{35}{37}$
3. $\frac{8}{17}$
4. $\frac{21}{29}$
5. $\frac{4}{3}$
6. $\frac{3}{4}$
7. Missing Side=12; Sin A=$\frac{3}{5}$; Cos A=$\frac{4}{5}$; Tan A=$\frac{3}{4}$
8. Missing Side=8; Sin A=$\frac{4}{5}$; Cos A=$\frac{3}{5}$; Tan A=$\frac{4}{3}$