Question

find the missing side of each triangle. round your answers to the nearest tenth if necessary.
3)
triangle with legs 21 and 20, hypotenuse x
4)
triangle with leg 75, hypotenuse 85, leg x
find the value of each trigonometric ratio to the nearest ten - thousandth.

1. cos a

right triangle abc with right angle at b, ab = 20, bc = 15, ac = 25

1. tan x

right triangle xyz with right angle at y, xy = 27, yz = 36, xz = 45

1. tan c

right triangle abc with right angle at b, ab = 14, bc = 48, ac = 50

1. sin a

right triangle abc with right angle at b, ab = 16, bc = 30, ac = 34

Explanation:

Step1: Apply Pythagorean theorem (Q3)

$x^2 + 20^2 = 21^2$
$x^2 = 21^2 - 20^2 = 441 - 400 = 41$
$x = \sqrt{41} \approx 6.4$

Step2: Apply Pythagorean theorem (Q4)

$75^2 + x^2 = 85^2$
$x^2 = 85^2 - 75^2 = 7225 - 5625 = 1600$
$x = \sqrt{1600} = 40$

Step3: Calculate $\cos A$ (Q5)

$\cos A = \frac{\text{adjacent to } A}{\text{hypotenuse}} = \frac{20}{25} = 0.8000$

Step4: Calculate $\tan X$ (Q6)

$\tan X = \frac{\text{opposite to } X}{\text{adjacent to } X} = \frac{36}{27} \approx 1.3333$

Step5: Calculate $\tan C$ (Q7)

$\tan C = \frac{\text{opposite to } C}{\text{adjacent to } C} = \frac{14}{48} \approx 0.2917$

Step6: Calculate $\sin A$ (Q8)

$\sin A = \frac{\text{opposite to } A}{\text{hypotenuse}} = \frac{30}{34} \approx 0.8824$

Answer:

1. $x \approx 6.4$
2. $x = 40$
3. $\cos A = 0.8000$
4. $\tan X \approx 1.3333$
5. $\tan C \approx 0.2917$
6. $\sin A \approx 0.8824$