Trigonometric Ratio: Find each trig ratio. Give your answer as a fraction in the simplest form.
Answers
SOLUTION:
We have to first find the third side of the triangle before finding the required trigonometric ratios...
∴ In triangle RST, by pythagoras theorem
RS² + ST² = RT²
==> (36)² + (15)² = RT²
==> 1,296 + 225 = RT²
==> RT = √1,521
==> RT = 39
Now, we have found the third side, I.e, 39 units.
∴ The trigonometric ratios are:-
1. Sin R = Opposite side/ Hypoyenuse
==> ST/RT = 15/39 = 5/13
2. Cos R = Adjacent side/ Hypotenuse
==> RS/RT = 36/39 = 12/13
3. Tan R = Opposite side/ Adjacent side
==> ST/RS = 15/36 = 5/12
4. Sin T = Opposite side/ Hypoyenuse
==> RS/RT = 36/39 = 12/13
5. Cos T = Adjacent side/ Hypotenuse
==> ST/ RT = 15/39 = 5/13
6. Tan T = Opposite side/ Adjacent side
==> RS/ ST = 36/15 = 12/5
Answer: 1. sin R = 0.42 4. sin T = 0.91
2.cos R = 0.91 5. cos T = 0.42
3. Tan R = 0.46 6. Tan T = 2.18
Step-by-step explanation:
- Formulas: sin x=Height/Hypotenuse
cos x=Base/Hypotenuse
tan x = Height/Base
- With respect to angle R:
height = ST = 15
Hypotenuse = RT = 36
(i) Step-1: Base = SR =
= √(Hypotenuse² - height²) [Applying Pythagoras's theorem]
= √(RT²-ST²) = √(36²-15²) = 32.73
(ii) Step-2: (1) sin R = ST/RT = 15/36 = 0.42
(2) cos R = SR/RT = 32.73/36 = 0.91
(3) Tan R = ST/SR = 15/32.73 = 0.46
- With respect to angle T:
height = SR = 32.73
Hypotenuse = RT = 36
Base = ST = 15
(1) sin T = SR/RT = 32.73/36 = 0.91
2) cos T = ST/RT = 15/36 = 0.42
(3) Tan T = SR/ST = 32.73/15 = 2.18