Finf the exact value of sin A and cos A where a = 9 and b = 10 and <c is a right angle
2 answers:
To solve for the longest side, the hypotenuse, you have to use the pythagorean theorem. It will be 10^2 + 9^2 = c^2. 100 + 81 =c^2.
c^2 = 181 so c = sqrt(181).
to find sin of A do opposite/hypotenuse which gives you 9/sqrt(181)
to find cos of A do adjacent/hypotenuse which gives you 10/sqrt(181)
c^2 = 181 so c = sqrt(181).
to find sin of A do opposite/hypotenuse which gives you 9/sqrt(181)
to find cos of A do adjacent/hypotenuse which gives you 10/sqrt(181)
Answer:
sin A = 0.6666666667 ≈ 0.67
cos A = 0.7407407407 ≈ 0.74
Step-by-step explanation:
The triangle above is a right angle triangle . Angle C is the angle 90°. we can use the cosine law for triangle to solve for side c.
c² = a² + b² - 2ab.cos(C)
a = 9
b = 10
C = 90°
c² = 9² + 10² - 2 × 9 × 10 cos( 90)
c² = 81 + 100 - 180 × 0
c² = 181
c = √181
c = 13.45362405 ≈ 13.5
Using sine rule
a/sin A = b/sin B = c/sin C
a = 9
b = 10
c = 13.5
C = 90°
9/sin A = 13.5/sin 90°
13.5 sin A = 9 × sin 90°
13.5 sin A = 9
sin A = 9/13.5
sin A = 0.6666666667
Use SOHCAHTOA principle to find cos A
cos A = b/c
cos A = 10/13.5
cos A = 0.7407407407
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Answer:
The correct option is;
No, The greater rate of change of Plant A will result in it being 0.9 inches taller in 6 weeks
Step-by-step explanation:
The parameters given are;
Plant A:
Weeks, Height
0, 3
1, 4.8
2, 6.6
3, 8.4
The rate of change of height, H per week, t, for plant A per week is therefore;
Therefore we have;
H = 1.8 × t + 3
At week 6,
H = 3 + 6×1.8 = 13.8 inches
Plant B
Weeks, Height
2, 7.3
3, 8.7
4, 10.1
The rate of change of height, H per week, t, for plant B per week is given as follows;
Therefore we have;
When t = 2, H = 7.3 hence, 7.3 = 2 × 1.4 + H₀
Where:
H₀ = H at t = 0
H₀ = 7.3 - 2 × 1.4 = 4.5
At week 6 we have;
H = 4.5 + 6×1.4 = 12.9 inches
Which indicates that Plant A will be 0.9 inches taller than Plant B at week 6.
The correct option is therefore;
No, The greater rate of change of Plant A will result in it being 0.9 inches taller in 6 weeks.