a To compute the perimeter of the given figure we need to know the unlabeled side as well. By adding a segment to the diagram we can create a right triangle where both legs are known.
Now we can find the hypotenuse of the right triangle by substituting the length of its two legs into the Pythagorean Theorem.
Now that we know the last side we can calculate the perimeter.
b Examining the right triangle, we see that an angle and its adjacent side are known. Since we want to find the opposite side of the angle, we must use the tangent ratio.
tan θ = Opposite/Adjacent
Let's look at the given diagram and substitute the given values into the above equation.
c Examining the diagram, we see that the hypotenuse and adjacent side to the angle labeled x are known. This means we have to use the cosine ratio to determine x.
cos θ = Adjacent/Hypotenuse
Let's look at the given diagram and substitute the given values into the above equation.
d Examining the diagram, we see that while the hypotenuse is unknown, the angle and the opposite side to it are known. This means we have to use the sine ratio to determine x.
sin θ = Opposite/Hypotenuse
Let's look at the given diagram and substitute the given values into the above equation.
In the right triangle, an angle and hypotenuse are known. Since we want to determine the angle's opposite side, we have to use the sine ratio to solve for h.
e Let's illustrate this situation in a diagram. We will call the height of the kite h.
We know an angle and the hypotenuse of the right triangle. Since we want to determine the angle's opposite side, we have to use the sine ratio to solve for h.
