FST Sections 5.1 and 13.1

3.14% of Sailors are PI rates!

b a c C B A Side c is called the hypotenuse. Side a is opposite of Angle A. Side a is adjacent to Angle B. Side b is opposite of Angle B. Side b is adjacent to Angle A.

b a c C B A

4 3 5 C B A

b a c

 When you have an angle and a side, and you are looking for a missing side of a right triangle, you should always use sin, cos, or tan (and then PT).  Pick sin, cos, or tan based on the information given in the triangle already – match this information to SOHCAHTOA to pick the correct ratio  In some cases, you’ll know two (or three) sides of a triangle. Then, you pick which ratio to use to find the angles.

5 x

x

x

Suppose that the distance along the slope from the top of the bank of a river to the edge of the water is 23.6 m, and a surveyor finds that the land slopes downward at an angle of 26 o from the horizontal. Find d, the horizontal distance from the top of the bank to the river’s edge m 26 o d

 In some cases, you’ll know two (or three) sides of a triangle. Then, you pick which ratio to use to find the angles.  Find an angle from a ratio??  How do we do that???

 Set up the equation as you did when solving for a missing side.  When done, you can use the PT and/or the CAT to check your answers (Pythagorean Theorem) (Complementary Angles Theorem)

 Use inverse sin (sin -1 ), inverse cos (cos -1 ), or inverse tan (tan -1 ) to determine angles when the side lengths are already known  You can find the inverse buttons as the 2 nd function on the sin, cos, and tan buttons on your calculators

 Always set the problems up as if you already know θ. We won’t switch to the inverse function until the end of the problem!!  Stick to SOHCAHTOA!! It’ll always work!!

8

9

 Angle of elevation: the angle rising up from the horizontal  Angle of depression: the angle going down from the horizontal θ Horizontal θ

Federal law specifies that every new public building must be accessible by a ramp with slope 1/12 or less. What is the maximum angle of elevation for a ramp?

A safe angle for a fire ladder is 65 o to the ground. To the nearest foot, how long must the ladder be to reach 19 feet up the side of a building?

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