Solutions to Right triangle trigonometry
1. Find x.
Solution: We have x
15
=sin 30◦.
So, x =15 sin 30◦=15
2=7.5.
2. Find x.
Solution: Note that 9
x
=cos 20◦.
So, x cos 20◦=9, meaning x =9
cos 20◦≈9.578.
3. Find x.
Solution: Note that x
55
=tan 30◦.
So, x =55 tan 30◦=55√3
3≈31.75.
4. Suppose you know a flagpole is 30.5feet away from you, and the angle of elevation to the
top of the flagpole is a 40 degrees. How tall is the flagpole?
Solution: Let x be the height of the flagpole. Then x/30.5 =tan 40◦. We get, x =30.5tan 40◦≈
25.59. So, the height is about 25.59 feet.
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