Question

1. In ΔPQR, sin P = 0.3, sin R = 0.8 and r = 16. Find the length of p.

2. In ΔABC, m < B = 45°, m < C = 38° and a = 30. Find the length of b to the nearest tenth.



3. In ΔPQR, sin P = 0.4, sin R = 0.8 and r = 10. Find the length of p.



4. In ΔABC, m < B = 42°, m < C = 30° and a = 22. Find the length of b to the nearest tenth.



5. In ΔRST, m < R = 102°, r = 38, and t = 30. Find the m < S, to nearest degree.



6. In ΔPQR, sin P = 0.6, sin R = 0.9 and r = 20. Find the length of p.



7. In ΔABC, m < B = 32°, m < C = 38° and a = 22. Find the length of b to the nearest tenth.



8. In ΔPQR, sin P = 0.9, sin R = 0.8 and r = 22. Find the length of p.

Answer 1

Explanation:

1. We know r and p are not the hypotenuse since sin can't be used on an angle where the opposite side is a hypotenuse. This means that q is the hypotenuse. If we use the known side length r, we can use the equation

sin(r) = r/q ; 0.8 = 16/q ; q = 16/0.8 ; q = 20

Now that we know q is equal to 20, we can use that in finding p:

sin(p) = p/q ; 0.3 = p/20 ; p = 20(0.3) ; p = 6. This is the length of p.

2. To find b, we can use sine. First we need m<A, which is 97. 180 - (45 + 38) = 97. Clearly a=30 is the hypotenuse, since A is the greatest angle.

sin(B) = b/a ; sin(38) = b/30 ; b = 30(sin(38)) ; b = 18.47

3. Like the first question, we know r and p are not the hypotenuse. This means using r will be necessary again.

sin(R) = r/q ; 0.8 = 10/q ; q = 10/0.8 ; q = 12.5

Now we use sin P again:

sin(P) = p/q ; 0.4 = p/12.5 ; p = 12.5(0.4) ; p = 5.

4. sin(B) = b/a ; sin(42) = b/22 ; b = 22(sin(42)) ; b = 14.7

5. tan(Θ) = t/r ; Θ = tan^-1(30/38) ; Θ = 38 degrees

6. sin(R) = r/q ; 0.9 = 20/q ; q = 20/0.9 ; q = 22.22

sin(P) = p/q ; 0.6 = p/22.22 ; p = 22.22(0.6) = 13.33

7. sin(B) = b/a ; sin(32) = b/22 ; b = 22(sin(32)) ; b = 11.7

8. sin(R) = r/q ; 0.8 = 22/q ; q = 22/0.8 ; q = 27.5

sin(P) = p/q ; 0.9 = p/27.5 ; 27.5(0.9) ; p = 24.75