Using the illustration, find the measure of each acute angle for the right triangle.
a = 38.0 m, b = 60.1 m
To find the measure of each acute angle in a right triangle, you can use trigonometric ratios. In this case, we can use the sine and cosine ratios.
Let's assume that angle A is the acute angle opposite side a, and angle B is the acute angle opposite side b.
Using the sine ratio:
sin(A) = opp/hyp = a/c
sin(A) = 38.0m / 60.1m ≈ 0.632
A ≈ sin^(-1)(0.632)
A ≈ 39.7°
Using the cosine ratio:
cos(A) = adj/hyp = b/c
cos(A) = 60.1 m / 60.1 m = 1
A ≈ cos^(-1)(1)
A ≈ 0°
Since angle A is opposite side a, which is longer than side b, it means that angle A is the larger acute angle.
Therefore, the measure of the larger acute angle in this right triangle is approximately 39.7°, and the measure of the smaller acute angle is approximately 0°.
To find the measure of each acute angle in the right triangle, we can use trigonometric ratios such as sine, cosine, and tangent.
Given the lengths of the two sides of the triangle, a = 38.0 m and b = 60.1 m, we can use the following trigonometric ratios:
1. Sine (sinθ) = opposite/hypotenuse
2. Cosine (cosθ) = adjacent/hypotenuse
3. Tangent (tanθ) = opposite/adjacent
In this case, the sides a and b correspond to the opposite and adjacent sides of the triangle, respectively.
Using sine:
sin(θ) = opposite/hypotenuse
sin(θ) = a/b
sin(θ) = 38.0 m/60.1 m
sin(θ) = 0.632
To find the angle θ, we need to take the inverse sine (also known as arcsine) of 0.632:
θ = sin^(-1)(0.632)
θ ≈ 39.928 degrees
Using cosine:
cos(θ) = adjacent/hypotenuse
cos(θ) = b/a
cos(θ) = 60.1 m/38.0 m
cos(θ) = 1.579
To find the angle θ, we need to take the inverse cosine (also known as arccosine) of 1.579:
θ = cos^(-1)(1.579)
θ ≈ 53.837 degrees
Therefore, the measures of each acute angle for the right triangle are approximately 39.928 degrees and 53.837 degrees.
To find the measure of each acute angle in a right triangle with given side lengths, you can use trigonometric ratios.
Given:
a = 38.0 m
b = 60.1 m
First, let's label the sides of the right triangle. In a right triangle, one angle is 90 degrees (a right angle) and the remaining two angles are acute angles.
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a |
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b |
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Using the Pythagorean theorem, we can find the length of the third side (the hypotenuse, c).
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):
c^2 = a^2 + b^2
Substituting the given values:
c^2 = 38.0^2 + 60.1^2
c^2 = 1444 + 3612.01
c^2 = 5056.01
Taking the square root of both sides, we find:
c ≈ √5056.01
c ≈ 71.10 m
The acute angles in a right triangle can be found using trigonometric ratios. The most commonly used ratios are the sine, cosine, and tangent.
In this triangle, we can use the sine ratio to find the measure of one of the acute angles (θ) adjacent to side a.
sin(θ) = a / c
sin(θ) = 38.0 / 71.10
sin(θ) ≈ 0.5349
To find the angle θ, we can find the inverse sine of the value obtained.
θ ≈ arcsin(0.5349)
θ ≈ 31.310 degrees
Therefore, one of the acute angles in the right triangle is approximately 31.310 degrees. The other acute angle is 90 degrees (as it is a right triangle), so the measure of the remaining acute angle is 180 - 31.310 - 90 = 58.690 degrees.