Question

Please help me with this question

Answer 1

Answer:

• y is 10.9

• theta is 65.4°

• Alpha is 24.64°

• sin theta is 10.9/12

• COS theta is 5/12

• tan theta is 10.9/5

• csc theta is 12/10.9

• ces is 12/5

• cot theta is 5/10.9

Step-by-step explanation:

Solution 1

Using the Pythagorean theorem

c²= a² + b², where c is the hypotenuse , a And b are the sides.

12² = y² + 5²

144 = y² + 25

144 - 25 = y²

√119 = √y²

10.9 = y

y is 10.9

Solution 2

Using SOH-CAH-TOA

COS theta = Adjacent/Hypothesis

COS theta = 5/12

COS theta = 0.417

theta = COS-1 0.417

theta = 65.4°

theta is 65.4°

Solution 3

We are dealing with right triangle and it sum is 90.

To find Alpha subtract theta for 90

Alpha = 90 - 65.4 = 24.64°

Therefore Alpha is 24.64°

Solution 4

Using SOH-CAH-TOA

sin theta = opposite/ hypotenuse

sin theta = 10.9/12

sin theta is 10.9/12

Solution 5

Using SOH-CAH-TOA

COS theta = Adjacent/Hypothesis

COS theta = 5/12

COS theta is 5/12

Solution 6

Using SOH-CAH-TOA

tan theta = opposite/adjacent

tan theta = 10.9/5

tan theta is 10.9/5

Solution 7

csc theta is the reciprocal of sin theta

csc theta = 12/10.9

csc theta is 12/10.9

solution 8

ces theta is the reciprocal of COS theta.

ces theta = 12/5

ces is 12/5

Solution 9

cot theta is the reciprocal of tan theta

cot theta = 5/ 10.9

cot theta is 5/10.9

Answer 2

Answer:

• y = √119 ≈ 10.909
• θ ≈ 65.376°
• α ≈ 24.624°
• sin(θ) = (√119)/12 ≈ 0.909059
• cos(θ) = 5/12 ≈ 0.416667
• tan(θ) = (√119)/5 ≈ 2.181742
• csc(θ) = (12√119)/119 ≈ 1.100038
• sec(θ) = 2.4
• cot(θ) = (5√119)/119 ≈ 0.458349

Step-by-step explanation:

You can use the Law of Cosines after you find y or θ. Using the given information, you can apply the Pythagorean theorem, the Law of Sines, or the definition of the cosine trig function.

The mnemonic SOH CAH TOA is intended to remind you of the relations between sides and angles in a right triangle. It tells you ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

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find y

The Pythagorean theorem relates the measures of the sides. It tells you ...

  y² +5² = 12²

  y = √(144 -25) = √119

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find angles

The trig relations above tell you ...

  sin(α) = 5/12   ⇒   α = arcsin(5/12) ≈ 24.624°

 cos(θ) = 5/12   ⇒   θ = arccos(5/12) ≈ 65.376°

Of course, once you find one of the angles, you can find the other. The sum of the two acute angles in a right triangle is 90°.

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find trig functions

Using the definitions above for the trig functions, you have ...

  sin(θ) = y/12 = (√119)/12

  cos(θ) = 5/12

  tan(θ) = y/5 = (√119)/5

Using trig identities, you have ...

  csc(θ) = 1/sin(θ) = 12/√119 = (12√119)/119

  sec(θ) = 1/cos(θ) = 12/5 = 2.4

  cot(θ) = 1/tan(θ) = 5/√119 = (5√119)/119

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Additional comment

The attached calculator screen shot shows you the angle θ on the first line, and the value of y on the second line. The csc, sec, and cot are shown on the third line. You will notice the angle mode (DEG) is seen in the lower left corner. If the calculator angle mode is set to radians, you will see the angles as relatively small radian values: θ ≈ 1.141, α ≈ 0.4298.

We have shown both exact values and decimal values you can round to the desired precision.