Answer:
so, question 1, label the sides given, the side opposite to the right angle is the hypotenuse, as its the longest side, then the bottom line is the adjacent line, as it has both the angle and the right angle, and the remaining side, which is opposite the 0 is the 'opposite'.
question 2- the values of cos(θ) and tan(θ) are 4/5 and 3/4
explanation below:
if sin(θ) = 3/5, we can use the pythagorean identity to find cos(θ) and tan(θ).
Given sin(θ) = 3/5, we can find cos(θ):
cos^2(θ) = 1 - sin^2(θ)
cos^2(θ) = 1 - (3/5)^2
cos^2(θ) = 1 - 9/25
cos^2(θ) = 16/25
Now, taking the square root of both sides to find cos(θ):
cos(θ) = ±√(16/25)
Since cosine is positive in the first and fourth quadrants, we take the positive square root:
cos(θ) = √(16/25) = 4/5
Next, we can find tan(θ):
tan(θ) = sin(θ) / cos(θ)
tan(θ) = (3/5) / (4/5)
tan(θ) = 3/5 * 5/4
tan(θ) = 3/4
so, the values of cos(θ) and tan(θ) are 4/5 and 3/4.
question 3-
sin(28°) ≈ 0.469 cos(46°) ≈ 0.719
question 4- find a to the nearest degrees
sinA =A ≈ 45.5°. tanA=49°
4- find x to one decimal place-
a- x=10.88
explanation-
tan(θ) = O / A
Given that the opposite angle (θ) is 55 degrees and the adjacent side (A) is 6.5, we can plug in these values:
tan(55°) = x / 6.5
Now, we can solve for x:
x = 6.5 * tan(55°)
Using a calculator, the approximate value of x is:
x ≈ 10.88
b- x= 9.323
explanation-
cos(θ) = A / H
where θ is the angle, A is the adjacent side, and H is the hypotenuse.
Given that the angle (θ) is 38 degrees and the adjacent side (A) is 7.4, we can plug in these values:
cos(38°) = 7.4 / H
Now, we can solve for H:
H = 7.4 / cos(38°)
Using a calculator, the approximate value of H is:
H ≈ 9.323
question 5-
a- θ ≈ 45°
Step-by-step explanation:
cos(θ) = A / H
where θ is the angle, A is the adjacent side, and H is the hypotenuse.
Given that the adjacent side (A) is 11.9 and the hypotenuse (H) is 15.6, we can plug in these values:
cos(θ) = 11.9 / 15.6
Now, we can find θ
θ = cos^(-1)(11.9 / 15.6)
Using a calculator, the approximate value of θ in degrees is:
θ ≈ 44.6°
So, the value of θ to the nearest degree is approximately 45°
b- θ ≈67°
explanation-
tan(θ) = O / A
where θ is the angle, O is the opposite side, and A is the adjacent side.
Given that the hypotenuse (H) is 13, the adjacent side (A) is 5, and the opposite side (O) is 12, we can use the Pythagorean theorem to find the missing side:
H^2 = A^2 + O^2
13^2 = 5^2 + 12^2
169 = 25 + 144
169 = 169
Now, we can find θ
tan(θ) = O / A
tan(θ) = 12 /
Now, find the inverse tangent (tan^(-1)) of both sides:
θ = tan^(-1)(12 / 5)
Using a calculator, the approximate value of θ in degrees is:
θ ≈ 67.38°
So, the value of θ, to the nearest degree, is approximately 67°.
hope that helps <33