Use a table of trigonometric values to find the angle θ in the right triangle in the following problem. Round to the nearest degree, if necessary.

cos θ = 0.9659 A = ? H = 20

I pitched those tables over 25 years ago, just about every cheap calculator can do trig.

cos Ø = .9659
Ø = 15°

Since I can't see your diagram , you will have to decide whether to use the sine or the cosine of 15° to find the rest

Use a table of trigonometric values to find the angle θ in the right triangle in the following problem. Round to the nearest degree, if necessary.

tan θ = ? O = 9 A = 15

Use a table of trigonometric values to find the angle θ in the right triangle in the following problem. Round to the nearest degree, if necessary.

sin θ = 0.7071 O = 5 H = ?

Well, well, well! Looks like we have a right triangle and we need to find an angle θ. We know that cos θ is 0.9659, and we need to find the adjacent side A. The hypotenuse H is given as 20. Let's break out the trigonometric values and see if we can clown our way to a solution!

Using the cosine function, we know that cos θ = adjacent/hypotenuse. So in this case, we have:

A/20 = 0.9659

To find A, we can multiply both sides of the equation by 20:

A = 0.9659 * 20

Now, let's do some clown math:

A = 19.318

Rounding to the nearest degree, we get A ≈ 19 degrees.

So the angle θ in the right triangle is approximately 19 degrees.

To find the angle θ in a right triangle when the cosine (cos θ) is given, we can use the inverse cosine function (also known as the arccosine function or cos⁻¹).

In this case, we have cos θ = 0.9659. To find θ, we need to find the inverse cosine of 0.9659.

However, before we proceed, we need to determine which quadrant θ lies in. Since the cosine is positive (0.9659 > 0), we know that θ is in either the first quadrant (0° to 90°) or the fourth quadrant (270° to 360°).

To determine the actual value of θ, we can use a table of trigonometric values or use a calculator with an inverse cosine function.

Using a table:
1. Look for the closest value to 0.9659 in the cosine column of the table. Let's say it is 0.966.
2. Find the corresponding angle value in the angle column. The angle closest to 0.966 in the cosine column is approximately 15.0°.

So, we can round the angle θ to the nearest degree as 15°.

Using a calculator:
1. Enter 0.9659 into the calculator.
2. Press the inverse cosine function, usually denoted as "cos⁻¹" or "arccos".
3. The calculator will give you the angle in radians. To convert it to degrees, multiply by 180/π (approximately 57.3°).
4. Round the result to the nearest degree.

Using the calculator approach, you would find that the angle θ is approximately 14.7°.

Therefore, rounding to the nearest degree, we can say that the angle θ is approximately 15°.