Bronte Wells
The measure of angle C is most likely 38°. In geometry, the sum of the angles in a triangle is 180°. If angle C is one of the angles in a triangle, we can find its measure by using the equation: C=180°−(A+B), where A and B are the other two angles of the triangle. 38° is a viable option when considering the properties of triangle angles.
| Characteristics | Values |
|---|---|
| Angle C | 42.8° |
| Angle A | 48° |
| Angle B | 42° |
| Angle D | 90° |
| Angle E | 48° |
| Angle F | 42° |
| Complementary Angle | 50° |
| Angle BCD | 74° |
| Angle D | 117° |
| Angle R | 37° |
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What You'll Learn
The measure of angle C is 42.8°
Triangle ABC is a right-angled isosceles triangle with side lengths of 38, 76, and 152. We know that in any right-angled triangle, one of the angles is always 90 degrees. In this case, angle C is the right angle, and its measure is 90°. The remaining two angles, angles A and B, are equal in measure since the triangle is isosceles. To find their measure, we can use the fact that the sum of all angles in any triangle is always 180°.
So, we have:
A + B + C = 180°
We know that C = 90°, so:
A + B = 90°
Now, since angles A and B are equal in measure, we can say:
A = B = x (let x be their common measure)
Therefore:
2x = 90°
X = 45°
So, the measure of angles A and B is 45° each.
Now, let's focus on angle C. Although we know its measure is 90°, we can still practice finding the measure of a non-right angle in this triangle. Let's assume angle C is not a right angle, and we want to find its measure. We can use trigonometric functions to find the measure of angle C. Let's use the sine function. We know that the side opposite angle C is 38, and the hypotenuse is 152. The sine of angle C is given by:
Sin(C) = opposite side / hypotenuse
Sin(C) = 38 / 152
Using a calculator, we find that sin^(-1)(0.25) is approximately 14.5°, which is the measure of angle C.
Now, let's consider a variation of this problem. What if the length of the side opposite angle C is 42.8 units, while the sides given as 76 and 152 remain unchanged? In this case, we can still use trigonometry to find the measure of angle C. We know that the sine of angle C is defined as the ratio of the side opposite the angle to the hypotenuse:
Sin(C) = opposite / hypotenuse
Plugging in the values, we get:
Sin(C) = 42.8 / 152
Using a calculator, we can find the inverse sine of this ratio to obtain the measure of angle C. The inverse sine of 0.2815 is approximately 16.05°. So, the measure of angle C is indeed very close to 15°, but it's slightly larger. This small difference in angle measure corresponds to a change in the length of the side opposite the angle, demonstrating the relationship between side lengths and angles in right triangles.
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Triangle ABC is an isosceles right triangle
First, let's recall some key facts about angles in triangles. In any triangle, the sum of the measures of all three angles is always 180°. Additionally, in a right triangle, one of the angles is always a right angle, which measures 90°. In this case, we know that angle C of Triangle ABC is the right angle, so angle C measures 90°.
Now, let's focus on the remaining two angles, angles A and B. In an isosceles triangle, the two sides of the triangle are equal in length, and consequently, the base angles (angles A and B) are equal in measure. Therefore, angles A and B have the same measure, and this measure can be calculated by subtracting the sum of the measures of angles A and B from 180° (the sum of all angles in a triangle). So, we have:
> 180° - (angle A + angle B) = angle C
> 180° - (90° + 90°) =
> 180° - 180° = 0°
However, we know that angle C measures 90°, so there seems to be a contradiction. This is because we're dealing with vertical angles, which are formed by the intersection of two lines and share the same measure. In this case, the 0° value we calculated is one of the vertical angles corresponding to angle C.
To find the measure of angle C, we can use the fact that the sum of the angles in the triangle must equal 180°. We already know angle C measures 90°, so we can set up the equation:
180° = angle A + angle B + 90°
Now, we can simplify and solve for the sum of angles A and B:
180° - 90° = angle A + angle B
90° = angle A + angle B
Since angles A and B are equal in measure in an isosceles triangle, we can divide both sides of the equation by 2 to find the measure of each angle:
90° / 2 = angle A or angle B
45° = angle A
45° = angle B
So, in Triangle ABC, angle A and angle B each measure 45°, and angle C measures 90°. Therefore, the measure of angle C in this isosceles right triangle is 90°.
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$7.19
The measure of complementary angles adds up to 90°
Two angles that add up to 90 degrees are known as complementary angles. For example, 30 degrees and 60 degrees are complementary angles as they add up to form a right angle of 90 degrees. When considered separately, these are referred to as complementary angles. However, when considered together, they form a right angle.
Adjacent complementary angles are those that have a common vertex and together make a right angle. For example, if angle AXB is a right angle, then angles BXC and CXD are considered complementary as they add up to 90 degrees. Non-adjacent complementary angles, on the other hand, do not share a common vertex but still add up to make a right angle. For instance, angles ABC and QPR each measure 40 and 50 degrees, respectively, and add up to 90 degrees, making them complementary angles.
The concept of complementary angles is closely related to supplementary angles. While complementary angles deal with angles that add up to 90 degrees, supplementary angles are concerned with angles that add up to 180 degrees, forming a straight line. For example, if one angle measures 70 degrees, its supplement would be 180 degrees – 70 degrees, resulting in a complementary angle of 110 degrees.
In trigonometry, complementary angles are used for trigonometric ratios. When one ratio is complementary to another by 90 degrees, the trigonometric functions of one angle are equal to the co-functions of the complementary angle. For example, sin (90° – A) is equal to cos A, and cos (90° – A) is equal to sin A. This relationship allows for easy calculations and conversions between different trigonometric functions.
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The measure of angle BCD is 74°
The given angle, angle BCD, is formed by extending one side of the radius of the circle, creating a straight angle with the radius as one ray, and the extended line as the other. In this case, the radius is BD, and the extended line is a continuation of this line beyond the circle. The vertex of the angle is point B, which is where the radius intersects with the circle.
The measure of an angle is the degree of the rotation of one arm of the angle from the other, and this is measured in degrees (°). The symbol for degrees is a small circle, and this is written after the number of degrees, with no space between. For example, 74 degrees is written as 74°.
To measure an angle, a protractor is used. A protractor is a semi-circular tool with degree measurements marked along its curved edge. The centre point of the protractor is placed on the vertex of the angle, and the base line of the protractor is lined up with one ray of the angle. The measurement of the angle is then read from the protractor by seeing where the second ray of the angle intersects with the protractor.
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Cubic centimetre and millilitre are the same measurements
A cubic centimetre, also written as cm³, cu cm, cc, or ccm, is a unit of volume. It is equal to the volume of a cube with one-centimetre sides. In the metric system, "centi" is the prefix for hundredths, or 10^-2. One cubic centimetre is equal to about 0.061 cubic inches.
A millilitre, sometimes written as millilitre, is also a unit of volume. It is equal to one cubic centimetre or 1/1000 of a litre. This is also approximately 0.061 cubic inches. In the metric system, "milli" is the prefix for thousandths, or 10^-3.
Therefore, one cubic centimetre is equal in volume to one millilitre. They are the same measurement, just with different names. The cubic centimetre is a multiple of the cubic metre, which is the SI-derived unit for volume. Similarly, the millilitre is an SI unit of volume in the metric system.
To summarise, the cubic centimetre and the millilitre are interchangeable. They are both measurements of volume that are equal to the volume of a cube with one-centimetre sides or 1/1000 of a litre.
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Frequently asked questions
42.8°
0.752 radians
Two complementary angles add up to 90°
