Question

Find the values of sin e, cos e, and tan e for the given right triangle. Give the exact values.sin ecos Ꮎ =tan =

Answer 1

For the sine and cosine of this angle, we need to know the hypotenuse of this triangle. To calculate the hypotenuse of this triangle, we can use the Pythagorean Theorem.

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

If we call the length of the hypotenuse as h, by the Pythagorean theorem we have

`\begin{gathered} 7^2+8^2=h^2 \\ 49+64=h^2 \\ 113=h^2 \\ h=\sqrt[]{113} \end{gathered}`

In a right triangle, the sine function of an angle is given by the ratio between the opposite leg and the hypotenuse. Using this property in our problem, we have

`\sin (\theta)=\frac{8}{\sqrt[]{113}}`

In a right triangle, the cosine function of an angle is given by the ratio between the adjacent leg and the hypotenuse. Using this property in our problem, we have

`\cos (\theta)=\frac{7}{\sqrt[]{113}}`