A right triangle has a hypotenuse of length 2.00 m, and one of its angles is 24.0°. What are the lengths of the following sides?
(a) the side opposite the 24.0° angle
(b) the side adjacent to the 24.0° angle
nope. Trig, geometry, or a good algebra II course
Oscar Had A Headache Over Algebra.
Sin x = Opp/ Hyp
Cos x = Adj/ Hyp
Tan = Opp/ Adj
Opp = 2 sin24
Adj = 2 cos24
I need hlep
To find the lengths of the sides of a right triangle, we can use trigonometric ratios: sine, cosine, and tangent.
(a) The side opposite the 24.0° angle is the side we need to find. Let's call it side A.
To find side A, we can use the sine ratio. The sine ratio states that the sine of an angle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse.
In this case, we know the hypotenuse is 2.00 m and we want to find side A. We can set up the equation as follows:
sin(24°) = side A / 2.00
Now, we can solve for side A by multiplying both sides of the equation by 2.00:
side A = 2.00 * sin(24°)
Using a calculator, we can find that sin(24°) is approximately 0.4067. Let's substitute this value into the equation:
side A = 2.00 * 0.4067
Calculating this, we get:
side A ≈ 0.813 m
Therefore, the length of the side opposite the 24.0° angle is approximately 0.813 m.
(b) The side adjacent to the 24.0° angle is the remaining side of the right triangle. Let's call it side B.
To find side B, we can use the cosine ratio. The cosine ratio states that the cosine of an angle is equal to the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
In this case, we know the hypotenuse is 2.00 m and we want to find side B. We can set up the equation as follows:
cos(24°) = side B / 2.00
Now, we can solve for side B by multiplying both sides of the equation by 2.00:
side B = 2.00 * cos(24°)
Using a calculator, we can find that cos(24°) is approximately 0.9135. Let's substitute this value into the equation:
side B = 2.00 * 0.9135
Calculating this, we get:
side B ≈ 1.827 m
Therefore, the length of the side adjacent to the 24.0° angle is approximately 1.827 m.