Question

First use the Pythagorean theorem to find the exact length of the missing side. Then find the exact values of the six trigonometric functions for angle

Answer 1

To determine the missing side of a right triangle, the Pythagorean theorem is used. This helps to find the exact length after which trigonometric functions such as sine, cosine, and tangent can be calculated for a given angle using the side lengths.

Step-by-step explanation:

To find the length of the missing side of a right triangle, we will first use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is: a² + b² = c², or solving for c, c = √a² + b². Once we have the length of c, we can find the six trigonometric functions for the specified angle as follows:

• Sine (θ) = opposite/hypotenuse
• Cosine (θ) = adjacent/hypotenuse
• Tangent (θ) = opposite/adjacent
• Cosecant (θ) = 1/sine (θ)
• Secant (θ) = 1/cosine (θ)
• Cotangent (θ) = 1/tangent (θ)

These functions are based on the angles and sides of the right triangle. By knowing the lengths of two sides, we can calculate these trigonometric ratios to find the exact values for the six trigonometric functions for an angle.

Answer 2

From Pythagorean theorem

`\begin{gathered} \text{hyp}^2=opp^2+adj^2 \\ \text{hyp}^2=20^2+21^2 \\ \text{hyp}^2=400+441 \\ \text{hyp}^2=841 \\ \text{hyp}=\sqrt[\square]{841} \\ \text{hyp}=29 \end{gathered}`

So the hypotenuse = 29

Now let's find the six trigonemetric