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# Angles and Trigonometric Ratios (need help with these questions ASAP)

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1. What is measure of angle A? 2. What is measure of angle P? 3. What is the measure of angle C? 4. What is the measure of ∠L ? 5. A board is leaning against a vertical wall. The board makes a 62° angle with the ground and touches the wall at a point that is 45 in. above the ground. What is the length of the board, rounded to the nearest inch?

24 in.

40 in.

51 in.

96 in.

Mar 13, 2018

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These are all basically the same type question involving trig ratios

remember   S-O-H-C-A-T-O-A

which stands for, in right triangles.

sin = opposite side / hypotenuse

Let's do the first one...then you try the rest....

Looking for angle A    Opposite side is 4  hypotenuse is 5

SO the sin of angle A =  opposite/hypotenuse = 4/5

sin A = 4/5

then use your calculator to use 'ARCSIN'   (also called sin inverse) of 4/5

arcsin (4/5) = 53.13 degrees

You could also use cosine or tangent to find angle A

cos A = adjacent/hypotenuse  = 3/5      ARCOS (3/5) = 53.13 degrees

....or use the tangent

tangent = opposite/adjacent = 4/3    arctan (4/3) = 53.13 degrees

Now YOU try the others !   Good Luck ! Mar 13, 2018
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2.  We  can find  P  with the tangent inverse  (other inverse functions are also possible )

arctan (12/5)  = P = 67.38°

3.  C  = arctan (22/120) = 10.39°

4.  We know the adjacent side to L  and the hypotenuse.......the cosine inverse is the way to go, here

arccos ( 18/60)  = L  = 72.54°

5.   We know an angle an opposite side and we are looking for the hypotenuse

So.....the sine function is what we need

sin (62)  =  45 / hypotenuse     rearrange as

hypotenuse  = board length  =  45 / sin (62)   =  51 in   Mar 13, 2018