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 Up until this point our work with right triangles has dealt solely with the sides  Today we’re going to link the sides with the interior angles via one of the 6 trigonometric ratios  These ratios are vital to our understanding of trigonometric

In order to aptly define the trigonometric ratios, it’s essential to develop a naming scheme for the sides of a triangle It’s also imperative to remember that these side designations are reliant on the position of the angle in question, theta Adjacent Side θ Opposite Side Hypotenuse

The values for the tangent ratio can be found either via calculator or the table on page 925 Adjacent Side θ Opposite Side

Find the tangent of the angle, theta 15 θ 21

Find the tangent of theta

Using either the calculator or the table, we can find the numerical value of the sine and then use it to solve for missing sides o x You can enter this into the calculator to decrease rounding error

Solve for x

Find the perimeter

Solve for x

We can use our understanding of special triangles to find trigonometric ratios 1 60 o 2 30 o 45 o 1 1

Find the tan of 45

Solve for x

You are looking at an eye chart that is 20 feet away. Your eyes are level with the bottom of the “E” on the chart. To see the top of the “E”, you look up 1 o. How tall is the “E” A..35 in B..35 ft C. 5 in

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You are standing in the North stairwell and look out the window to see a car on the opposite side of 68 th street. The angle of declination is 55 o. If the car is 55’ from the edge of the building, how high off the ground are you?

Utilizing the tangent ratioUtilizing the tangent ratio