1-3 are about trigonometric ratios (SOH CAH TOA). 4, 5 are about the Law of Cosines, and 6 uses the Law of Sines.
1. Sin = Opposite/Hypotenuse
x = 10*sin(40°) ≈ 6.428
2. Sin = Opposite/Hypotenuse
x = arcsin(7/12) ≈ 35.69°
3. Tan = Opposite/Adjacent
x = 18/tan(52°) ≈ 14.063
4. b^2 = a^2 +c^2 -2ac*cos(B)
B = arccos((a^2 +c^2 -b^2)/(2ac)) = arccos((7^2 +13^2 -8^2)/(2*7*13))
B = arccos(11/13) ≈32.20°
5. Same formula.
x = √(a^2 +c^2 -2ab*cos(B)) = √(157-132cos(42°)) ≈ 7.675
6. The ratio of side lengths is the same as the ratio of the sines of the opposite angles.
6/10 = sin(x)/sin(100°)
x = arcsin((6/10)*sin(100°)) ≈ 36.22°
Answer:
2 i believe
Step-by-step explanation:
Answer: i) 30 students for chemistry
ii) 21 students for only one subject
iii) 61 students
Step-by-step explanation: from the question we got 30 students registered for chemistry. number students only for biology = (27-18) = 9
number of students only for chemistry = (30-18) = 12
number of student registered for only one subject = (12+9)= 21
number of students registered for neither two subjects = {100-(9+12+18)} = 61
Answer:
∠1 = ∠3 = 54°; ∠2 = 36°
Step-by-step explanation:
Each of the triangles is isosceles. Triangles opposite each other are congruent, so ∠2 is congruent to 36°.
∠2 and ∠3 are complementary, so ∠3 is 54°. Since ∠3 is congruent to ∠1, it, too, is 54°.
To put words into equations:
x+y+z =50
x=4y
4y=5z -> z= 4/5 y
Which means
4y+y+ 4/5 y= 50
29/5 y =50
29y=250
Y=29/250
